This is discrimination of opinion, strange as that sounds.
There is a reason we don't see signs up like; 'No Blacks', 'No Gays', 'No Jews' in private establishments. Its because its not allowed, we either have a list of protected groups - or a general rule that forbids banning anyone because of their 'group'.
If we don't fairly quickly extend free speech into these platforms, then we will have to eventually legislate a list of protected opinions.
So, I'm certain you will find legally hung signs with racist and discriminatory content in certain places.
> If we don't fairly quickly extend free speech into these platforms
That's outside the scope of the First Amendment. It may not even be possible to pass such a law without infringing on those platforms First Amendment rights... I would expect the SCOTUS to strike any such law down.
Could you imagine the immediate public backlash against this type of behavior by a private establishment? I don't think the law is doing the heavy lifting here.
A large number of people are still alive back from when Jim Crow laws were still actively in effect. In 1957 the president had to send the 101st airborne to Arkansas to escort black children to school and seized control of the state's national guard because they were being used to block desegregation of schools: https://en.wikipedia.org/wiki/Little_Rock_Nine
A non-trivial percentage of Americans would love to have these signs up and are kept from doing so by the law. The women's movement, LGBT rights, and minority rights are actually a fairly new thing, and are still not without controversy in the US.
As for your comment, the cake shop has a product they are letting people buy (in effect, serving them). They are willing to produce that product for a certain group of people for a certain activity (celebration of a state recognized marriage) based on their identity. They are not willing to produce that product for another group of people for the same activity (celebration of a state recognized marriage) based on that second group's identity. Now you can argue that the shop is within their rights to do that for religious reasons and the Supreme Court would agree with you, but it's still refusing service based on identity and you know it. If you want to split hairs and say they "refused to provide COMPARABLE service because they were gay" as the buyers may have been able to buy other products then so be it.
In the bakeshop case though, I do not think it has ever been alleged, that they ever refused to serve anyone cakes just for being gay. I think the whole case hinged on the question whether making a wedding cake is significantly more than just selling a cake off the shelf to anyone who comes in (I am really not sure if, as a matter of principle, private entities in a free society should be compelled to do business with anyone they do not want to, be that marrying gays or cynical coders who go by "Fins" though). So no,I don't think saying that they "refuse to serve gays" is a proper characterization.
It's the former. There is no law, at least in the US, that forbids banning people from private property for group membership in general.