Payment processors, webhosts, etc (I assume you're alluding a lot of the alt-right sights being removed from those platforms) have in practice refused to serve customers that expose them to legal culpability. There's a clear difference.
Yes. Bake the cake. The only legal culpability is to NOT do so.
What legal culpability do they have accepting payments for organizations that run websites that allow people to exercise their constitutionally protected rights to free speech?
Yes. Bake the cake. The only legal culpability is to NOT do so.