Religious liberty - in American law - certainly allows allow people to express their opposition to certain groups by withholding their services, banning them, or labeling them. The government, however, cannot perform these acts.

One cannot bring an action against someone for speaking out against certain groups unless that someone advocates some other illegal act such as assault, in which case the offense is advocating an illegal act.

Some of our Anglophone cousins in the Commonwealth go further because they lack a First Amendment and/or presume to be able to regulate religious beliefs and speech.

Oddly the very ground for Obergefell v. Hodges, privacy, is the primary basis for the freedom of association that underpins the American view of religious liberty.