Certainly - I don't deny that many of those regimes were secular. (though it's worth noting not all were)
Is it though? For that minority of regimes (and movements; let's also avoid the trap of assuming that terrible things are only carried out by governments) that were not secular, how important was their religious nature to the political murder that they were responsible for? Generally not at all; or about as relevant as the fact that the Nazis were
German Nationalists.
Now, I need to point out that I'm not bringing up the essentially secular nature of mass murder in the twentieth century as a way of bashing the nonreligious; that would be beyond absurd for several reasons (one that you are, of course, aware of; so I won't bother to lay them out). I pointed it out because I do not like this tendency to argue that conflicts about religion and between religions are somehow central to history or to religion's role in it. In any case I would tend to argue that religion is something that humans do, rather than a 'thing' that causes humans to do other things (be they good or bad).
Of course there's also the interesting issue of conflicts that are often
inaccurately ascribed religious motivation; the recent low level civil war in Northern Ireland would be a particularly good example of that. Other factors were at work, but because religion had become (for a complicated set of related factors) a marker of identity in the province, it was all that outside observers noticed; in part because doing so meant that they did not have to re-examine the complex relationships between Ulster (however defined) and the wider world. Though I suppose that counts as a digression (but then so does this entire discussion, such as it is, because whatever we are writing about it is not a film that I will never see).
Thinking a little further, perhaps that odd digression gets closer to what I'm attempting to get at than any actual attempts at a coherent explanation. Whenever the question of history emerges in a debate about religion (and it tends not to take very long) it is usually in a form that is horrifically reductionist. Not only that, but it denies agency (and so, in a way, absolves any responsibility) for anyone who isn't a special little snowflake of some kind or other.
