Can you find an example of this that isn't a phone company? Common carrier only applies to phone companies, it doesn't apply to CDNs, content providers in general, or websites.

I'll point out too that Verizon or AT&T can terminate services for other things. If your line is used to harass people or make prank phone calls then it can be shut down. Common carrier doesn't mean that they have to allow everyone to use their service.