A registrar or caching provider withdrawing service to a customer is essentially sending a message, and from that perspective the action should be covered by free speech. So I would argue that yes, if GoDaddy or Cloudflare were offended by Breitbart, they should be able to cut them off.
Note that in this case, the provider would not be infringing on the customer's free speech, because there are myriad other providers they can use.
If they were "sending a message" to a BLM or an LGBT group would you still support their rights to do so?
If the internet existed in the 1950's and the apparent (at least as a public face goes) vox populi would favor and crave for both self and institutionalized censorship as much as they do now the civil rights movement would've been dead in it's tracks.
It seems that people are busy yelling Nazi's Nazi's rather than having an actual good look at history.
When ever ideas are being silenced much much worse things tend to follow.
Yes I would. In fact I sided with the cake shop owners who didn't want to make a cake for a gay couple. They should have simply taken their business elsewhere, or made their own cake.
The fact that these guys can't find anyone (out of hundreds if not thousands of options) to host them is useful feedback about how opposed our free society is to their message.