Could you be FORCED to eat at say Chik Fil E even if you disagreed with their religious beliefs?
No, then why pray tell should they be FORCED to serve you if they don't agree with yours?
It's called discrimination. What if you decide you don't like black people, or Jews, or Italians. You cannot put up a sign which says "No blacks, Jews or Italians served". If you open your doors to the public, you must serve ALL members of the public even if they walk into your store wearing Nazi uniforms. Discrimination on the basis of race, creed, sex, or sexual orientation, is illegal.
If you don't like that law, you are quite free to find some other way of making your living that doesn't involve serving the general public.
That law is COMPLETELY unconstitutional.
You can't find ANYWHERE in the COTUS where the federal government is given the authority to tell people they can't discriminate.
You ESPECIALLY can't find anywhere that gives the government the authority to tell people they can discriminate, but not for certain reasons.
I own a business. I can hang a sign up that says
"No people who smell bad"
that's discrimination, but perfectly legal.
I can't hang up a sign that says
"no jews"
How is one discrimination any more of the federal government's business than the others?
You of course can not logically answer that question.