It is a 'public accommodation' within the meaning of the legal definition: i.e., a place where the general public may freely enter and do business. Civil rights law forbids discrimination in public accommodations on the basis of race, religion, or national origin. If a Christian baker said, we don't serve Jews, they'd get sued in a minute.

in what part it says sexual orientation though.?

Why not? If it's a service available to the public, it must be a public service, no?