Well that's the thing, sexual discrimination isn't really protected in the US outside of employment.
The US has:
- 14th Amendment, which states the law must apply to everyone equally (so gay people can get married)
- The Civil Rights Act, which contains various Titles:
- Title II, which prevents businesses in hospitality or operating across state lines from discriminating over race, color, religion, or national origin
- Title VI, which prohibits businesses working for the federal government from discriminating over race, color, or national origin
- Title VII, which prohibits employers from discriminating over race, color, religion, sex, or national origin
I'm actually in 2 minds about whether the 1st Amendment would prevent this. One the one hand, there is a clear gap in the Federal law that State law should be able to fill. On the other, that gap was exactly the same thing as the gay cake baker successfully challenged against.
Well that's just the futility of banning boycotts. Unless someone actually says they're boycotting, you'd have almost no way of proving that they were.