Bear too in mind they are removing content. Before this blew up in the media, did they have a problem hosting the stuff they're now removing?
I'm not convinced there's an argument that the right of a political cause to have its music distributed by a particular company trumps the right of a company not to distribute it or the right of the public to pressure the company into not distributing it.
If one is to impose upon on the freedom of actions of media distributors or the potentially-boycotting public (I'm not sure the latter is even possible), there had better be something pretty amazingly special about the cause that means their right to be heard trumps others' rights not to be the amplifier. I'm not sure any remotely compelling argument exists for neo-Naziism being a cause deserving of such special privileges or music distribution services being the sort of thing one should have an inalienable right to.
Just as I think that songs should be legally free to espouse racism, but that they shouldn't espouse racism.
Not arguing one way or the other but "music streaming services" is not too different from many other services which people expect to police content.
Perhaps considering whether the company holds a monopoly or near-monopoly on that media gateway is relevant.