You're free to exercise your religion, you're just not free to acquire a business license and operate under any hocus pocus framework you want.
But it seems that there is no federal law, as written, that prohibits discrimination of customers are a business based on sexual orientation. Not even federal employment laws seem to protect LGBT, except for federal employees
But the Supreme Court can establish a precedent that the existing federal laws that protect the enumerated classes of race, national origin, religion, sex, age, and disability also cover classes not enumerated (what criteria?). Doing so would then prevent states from operating pro-religion/anti-LGBT laws until the federal laws are modified to overturn the precedent by specifically excluding LGBT. It's not so unusual, Reed v. Reed (1971) extended the reach of this clause, and Romer v. Evans (1996) is a case that is strikingly similar to the current issue.
But until that happens, the issuing of business licenses is controlled at the State and County level and remains at their discretion as long as the federal guidelines are follow with regard to the enumerated protected classes. So if your State Assembly and Governor are into the same hocus pocus as you, you can all hold hands and triumphantly expel all the gays from your community. (no, not really going to play out that way. but that's what the end goal appears to be)
(that's how this arm-chair non-lawyer sees it)