“If, as they define themselves, are of the mind that God does not exist, then why all the vitriol?”
Because they do believe. They just have a problem with Him. They try to hurt God and his followers by repeatedly and publicly denying his existence in varying ways. That’s not all atheists but I do believe that describes the most vocal ones.
Indeed. Real atheists don't go around wasting their breath on a God they think is imaginary, but there are a lot of bitter God-haters out there who are pretending to be atheists.
Similarly, I don't doubt there are real homosexuals out there who merely have an attraction toward people of the same gender. But those kinds of people don't parade down the in drag to celebrate whichever bodily orifice they like to use -- that behavior is limited to people who want to be 'in your face' about flaunting common moral conventions, or also fall among the God-haters above.