It is illogical, but people do it all the time. Look at politics for example.
The evidence shows that Planned Parenthood is/was selling baby parts, but people like Hillary Clinton & Obama refuse to even look at the evidence.
Science shows that babies are human beings at conception, but people like the DNC Chair refuses to even acknowledge that her own children were human beings before they were born.
Other example:
It’s illogical to quit your job without having another one, especially when you have bills and responsibilities.
It’s illogical to smoke cigarettes, but that doesn’t stop people
It’s illogical not to wear a seatbelt, but people don’t.
it’s illogical to be a “new atheist” because it is impossible to prove that God does not exist (just like it’s impossible to prove that anything doesn’t exist), yet new atheists push their belief everyday. Belief that there is no God is more of a leap of faith than belief in God. There is physical evidence (scared scripture, other religions, etc.) to God’s existence, but the only “evidence” for no God is circumstantial evidence.
People do illogical things all the time. It’s what sets humans apart from Spock in Star Trek.
Our illogical behavior is a result of our free will and the fallen world.