Not sure. It is just my impression that SCOTUS has never ruled that it is unconstitutional to discriminate against gays in employment. It is not a suspect class. But I could be wrong. It does not come up much, because most states do ban such discrimination. Certainly the two states that I have lived in, CA and NY, do -obviously!
And I don't have a list of states that lack anti discrimination laws on their books when it comes to the LGBT community.
Anyway, I googled, and found
this. It comports with what you said.