If you believe Thor is the cause of lightning, you might be more willing to ignore meteorology. If you believe the Aesir are actually divine and walk between the worlds, you might be more willing to believe that some people are descendants of them and thus superior.

Jesus needs to sacrifice himself on the cross in order to satisfy the Old Laws and get everyone into heaven

If you believe that blood sacrifices hold power, you might think that some people are performing them when they aren't, or even perform them yourself.

If you believe the world will end, you might not be so concerned with maintaining it or even living in it.

My point is that making a habit of denying reality makes it easier to deny reality in the future, and even if one denial of reality is innocuous, later denials may not be. Bigots love to use religion to push racist, discriminatory, and abusive ideas, and the best way to defend against those ideas is to see how they align with reality. We can't identify harmful acts if we can't agree on the effect of an act, can we?

Anyway, the original topic was putting words in anti-theist's mouths. There's not even a generally accepted definition of anti-theism, with some being against organized religions, and others against monotheism specifically. To paint them all as opposite-christians is using a Zamboni as a brush.