So, you can be punished for refusing to make a cake for a gay wedding.
Well, hey, why not? No, really, we’re a democracy, they over the Pond are too, such laws can indeed be passed and they have been.
If you’re going to offer a service to the public then you’ve got to do so in a non-discriminatory manner*.
Twitter can and does ban people for saying entirely legal but unapproved of stuff. So, if you’re offering a service to the public you don’t have to do so in a non-discriminatory manner*.
Rather the point of this civil liberty, rule of law, sorta stuff is that it’s not discriminatory in this manner, isn’t it? We don’t divide into Good ‘uns and Bad ‘uns, those who gain the protection of the law and those who don’t. Rather, all are subject to the same law and laws.
*My own answer is that producers and providers can do what the fuck they like** on any grounds whatsoever, let the market sort it out. But that’s not the zeitgeist is it, despite being logically valid as a position?
** Who they provide to that is, not how, obviously. As with the publican, short measures are illegal but the right to ban anyone whenever, whatever, exists.