I do not know that any component of the Church fires people “just for being gay”.

Are you sure the accusation does not stem from someone parading in a “rights” parade or otherwise advocating against the Church’s teachings?

The exemption of churches from taxation is a common law inheritance from England. It is really not a result of statute, which defines business in a way that excludes churches.

An attempt to force churches to comply with so-called equal opportunity laws by holding its tax exemption hostage is considered by most legal experts as unlikely to pass constitutional muster due to the First Amendment.