Thinking about this, a couple of things occur to me.
As a gay, non-theist, white, male, living in a very Christian dominated place,
I find that the single biggest thing that irks me about revealed religion, which I am most familiar with, is the tendency to drag primitive ethics into the modern world.
From the racism and gender bigotry, to the homophobia, to the Divine Right of Kings, to that very fundamental concept of Abrahamic religion "The Chosen People". And the concept that we humans are born into a very low estate, due to the behavior of our distant ancestors, and must submit to and obey our betters hoping for some justice someday(generally after we're dead).
Oftentimes, modern Abrahamic religionists dump these Scriptural values and ethics. They do their best to retrofit modern secular morality into the ancient scriptures. That's a good thing, and quite common.
But it is not universal. Because the fundamental principle of revealed, Abrahamic, religion is to believe what self proclaimed spokesmen for God tell you to to believe. Pick the prophet you prefer, interpret his ancient writing as you prefer, and start insisting that your opinions are What God said...
That's what most irks me about theists. Attributing their personal opinions to God.
Another thing that seriously irks me about theists is their tendency to assume that everyone has their devotion to fallible human authority.
That's why "Darwinism" is such a thing. As though scientifically literate people believe in evolution because Darwin told them to do so, when we believe it because a mountain of evidence points towards "speciation through natural selection". Much of which Darwin didn't even know about, because the evidence didn't even appear until after he died. And then, mistaking Darwin for a prophet, they think that because Darwin was a Christian racist he was a racist due to science. When clearly he was a racist because he was a British Christian in the 19th century.
That's just a couple of the things that irk me about the theists who dominate the world I live in.
Tom