It is rare that one needs to speak up as an atheist and disown the speech or behavior of other atheists as communal hatred. Atheists are usually the smallest minority anywhere and where there is communal violence, they are usually on the receiving end, so the question of atheists being perpetrators of communal hatred rarely arises. There is the occasional Dawkins outrage, but it is not so relevant to India. However, there is extremism among atheists as well and today seems to be a good occasion to condemn and disown it as well.
Atheists often argue that there is no collective belief system called atheism. It is merely a lack of belief in God. It is true as far as it is a question of extrapolating the actions of one to others. However, the label itself confers a certain amount of shared traits - notably a stated disbelief in god. And while disbelief is an absence, the issue in extremism is rarely the belief or lack of it, it is the fervor in making the statement and imposing views on others. Atheists can cross the line between stating disbelief in god and religion to attacking a community based on their beliefs.
Like the beliefs of two atheists may have nothing in common, the beliefs of ISIS may have little in common with other Muslims as well. All atheists believe there is no God. That word play on disbelief being a lack of belief is well and good, it is also a belief about that lack. We aren't merely considering that there may be no God given the lack of evidence or that God is an unproven claim. We are certain that there isn't any God. We are not open to the possibility that there may be one (those are the agnostics). We aren't interested in exploring the possibility and potentially invalidating our claims. We define God by what we reject and ignore any interpretations of God that are saner. We are certain and see no need to contemplate alternatives as potentially viable.
Muslims believe there is one God and it is Allah and Mohammed is his messenger. Hindus have a diverse array of beliefs that can encompass countless gods or none. Christians believe there is one God and Jesus Christ is his son and so on. As an atheist, I must say there being no god is the logical conclusion of a contemplation of God as a sentient, omnipotent being. Belief in imaginary friends is not necessarily a bad thing, as long as it doesn't lead to denial that prevents well being. One simply projects what one believes is the best onto an imaginary external figure and gives it the authority we don't feel confident claiming as ourselves. I know there are lots that define God in a manner that makes sense to them and stay away from intentions and super powers. Indeed, a vivid imagination is necessary to creativity. I am sure, there are benefits. To others. I don't see the value.
No matter what a religious book says, the extent to which it is complied to by people always varies and the extent to which atheists engage with their disbelief also varies. For many, like me, it is a non-issue. God is absent. It doesn't take any space in daily life unless there is a requirement to analyze or discuss or state. Encountering someone expressing belief creates no urge to validate my own belief through convincing them into disbelief - a very similar process as seen in believers who tend to get you to believe in their Gods. It is no concern of mine whether you prefer God to Mickey Mouse. There are atheists who are more radical. They will not tolerate you being irrational and will strive to get you to .... um... see the light. Heck, there are atheist fundamentalists who won't tolerate "moderates" like me and expect us to do more to counter claims of God. To what end, I have no idea. Waste time over a non-existing creature even when fully aware it doesn't exist? What for?
Free Speech is a fundamental right. It is a bit dinged in India legally, and further butchered in practice. There are limitations by law or processes of engaging with the state. But apart from larger processes that are a part of belonging to an organized country, state, city, locality, home, etc that are established and a consequence of our social contract, while we do no harm to another, the assumption is that we have a legal right to speak, act and behave as we wish without being subject to impositions, limitations or harm. The rules are the same for all. Even when the laws have flaws and restrictions - typically those covering blasphemy - the understanding is that they are known to people up front and they apply to all (needless to say they get enforced with religious bias almost everywhere they exist). These are usually always facing a challenge, and rightfully so because they infringe on the right of disbelievers and critics to state their own views.
Free speech for atheists and in congruence with their "beliefs" typically ignores prohibitions on blasphemy where they exist and naturally includes the right to disagree about religion and God, to state their disbelief, to criticize the beliefs of other religions, including revered figures. We gleefully say, we are ok with you doing the same. Quite liberating, it is, to have nothing to defend. Turns out, the larger problem with religion - fundamentalist and communal violence - is a human trait and atheists are not immune to it either.
Communal hatred is not about our views or opinions - which in my view are acceptable regardless of being offensive. It is about people. It is the tantrum of the child being told there is no Santa. It is the tantrum of the child who proves Santa is better by calling Spiderman stupid, except these are adults with real power to inflict harm and when at the end of their ability to convince someone that Santa is better, are perfectly capable of harming someone for thinking Spiderman is better. Harm is not always physical. It can be emotional, social, economic. And when it targets the socially vulnerable and allies with others attacking them, it threatens to splinter social coherence for all.
There isn't any rational critique of religion when you comment on brutal ISIS beheadings that Muslims are taught to slaughter at an early age. You are simply letting your hatred for the Muslim community blind you into thinking of them as a monolith that acts in a manner you have associated in your mind with the worst of Muslims you hate. It isn't a rational critique of Hinduism to say Hindus burn their wives on funeral pyres or stigmatize widows. It is stereotyping of an entire community and reducing them to nothing but the nasty attributes you give them. It is not recognizing them as individuals, not even recognizing a diversity of compliance with your arbitrarily assigned trait.
And this is where atheism has its own brand of extremism and communal hate. It is a matter of rationality, whether our criticism is a logical evaluation of something or a statement of own belief or a statement of unfounded beliefs about other people (also known as fake news, if media does it). The last is not a fundamental right. I don't actually have a right to call you a scammer and hound you, taking every opportunity to discredit you and cause you emotional and possibly professional and economic harm from the consequences of my selectively interpreting your actions to fit my projection of you as a scam artist. That is stalking and harassment.
Just like knowing one atheist doesn't mean you know what all atheists do, selectively picking one Muslim or Hindu fanatic and calling all Muslims or Hindus fanatics based on that is the sign of an irrational mind that speaks more about paranoid delusions than skepticism or disbelief. Where does this hate come from?
Well, a lot of it from human nature. Unlike most identities associated with belief or a lack of belief, atheists are unique in the sense of their lack of belief having originated from different places and as a result of different circumstances. Some born to non-religious families are too.... vacant on the subject of belief to even qualify as atheists - they are more in the zone of that measuring scale not being relevant to them. Many others are a product of losing belief in a specific religion and its Gods and then learning to apply it to other gods. The religion of their origin can have a lot of anger or trauma attached to it, because they have suffered the disillusionment from it. In many cases, they may have suffered persecution as a result of it. Additionally, they may have stopped believing, but their experience as an insider gives them a unique insight into that religion and culture which allows them to make a more vigorous criticism of that religion more than others.
For example, I am no fan of Islam, but I can take it or leave it unless someone harms another. When they do act like absolute idiots, it still hurts me less than when Hindus do it. Because as someone born a Hindu Brahmin and who lacked belief in both religion and caste, but grew immersed in the culture, my own identity is mired in it. I know enough of the religion to hold a visceral anger against fundamentalists as those who enact the worst characteristics of the religion - that anger is a result of the betrayal of my painstakingly adopted values at the hands of the religion, not my lack of belief, which in itself is no reason for any particular emotion. That anger is because the acts of that brand of extremism caused me to have to reinvent my core identity as distinct from my roots. To consciously distance myself from aspects that I learned to feel ashamed of when I examined what the things I unthinkingly assumed to be "truth". In contrast, I don't feel anything about Islam. I haven't invested anything in it to feel cheated. I feel some for Buddhism because I spent half a decade as a part of a Buddhist family, so again, that feels like home culture and any wrong perpetrated in its name would make me feel violated. This will continue till I make my peace with it mentally. It is part of being human. Learning to recognize these influences rather than being an unthinking slave to them is a part of our philosophical evolution.
Similarly, Taslima Nasreen or Tarek Fatah (two ex-Muslim atheists) are vicious in their attacks on Islam and Muslims. I can understand that. They have had their trust broken by Islam. Taslima has been exiled from the country of her birth (and I think Tarek moved away on his own before they decided they didn't want him back). Needless to say, both have got plenty to be angry about on a personal level.
The problems arise when you believe your "insider" status as someone who was once a Muslim or Hindu gives you a unique insight into the case, but it actually isn't so and it is your hostility with the religion preventing you from seeing the observable reality. For example, like many upper caste Hindu men too fought for the rights of women and caste equality and widow remarriage, many Muslims are non-violent (to the point of being vegans), gentle, insightful souls. The vast majority of any identity is rarely acting in any manner similar to the extremist stereotype. In fact, extremists of all sorts have more in common with each other than the various identities they hijack. This is actually a no-brainer. if you take any diverse collective, the minute you stray the slightest from the definition of that collective, you stop being able to accurately describe its constituents. If an accurate description were possible, it would have already been included in the meaning of the word. And often, even the actual definition doesn't really fit.
Most people are born into their religion and had to do nothing, in particular, to "accept" it. So even core beliefs like "all Muslims believe in one God who is Allah" are actually up for debate depending on their conditioning. Most people aren't excessively religious and often kids grow up without any major belief and they are of the religion simply because that is part of the traditions of the family they belong to. Such a person may actually spend less part of their day thinking of their religion and what some holy book teaches than an atheist from it with a grudge or a zealous follower of another religion, who seeks validation of his beliefs being "right" by somehow proving others "wrong".
Regardless, there is a line. Atheism or rationalism cannot be the shoulder to fire guns of communal hatred from. Unlike religion, rationalism is not an identity, but a trait. If you make an irrational argument, sorry, you aren't being "a rationalist" no matter what you claim. Atheism is a lack of belief in God, not a set of beliefs about people who believe in that god.
Exploiting atheism and rationalism to conceal deep rooted hatred of specific communities is living in denial. There are terms - Islamophobia. Hindutvawadis recently helpfully invented "Hinduphobia". Use them.