Really? What "privileges" exactly are they asking for? Because I can point to quite a few laws in quite a few conservative states that make being trans something you can be fired for, that make acknowledging the existence of LGBT people something that can get teachers fired, that make it legal to refuse to serve LGBT people.
So: List the privileges that LGBT people are requesting, that are not available to straight or cisgendered people. This should be very easy given your statement.
They already have equal protection. What's being requested in law and other policy are additional privileges.