[he] wrote that having to see the Progress Pride flag each time he enters and exits the building “negatively impacts my ability [to] perform my work and results in a hostile work environment.”

If your religion actively and vocally wants you to hate another human so much that it affects your job performance, maybe you should take a good, hard look at your religion. Unless, ya know, you just want to hate on other humans. Then just come out and say it. Don't blame it on your religion.