I would probably prefer that the ISPs be a pipe. Pipes are agnostic to what flows through them.

Is an alt-right site espousing neo-nazi principles a terrorist site? Some might say so. Frankly, many would not. Is Planned Parenthood a terrorist site? I would not be surprised to see some ardent pro-lifers say "Damn skippy it is!".

Web hosting companies do make choices like that. They might ban sites providing bomb making instructions, or calling for open revolution, or so on. It's hard to do because there are so many. The best example would be cable TV pre-Internet. Companies like Comcast and Cablevision never regulated the content of programming. I could see everything from Nickelodeon to the Playboy channel. Nickelodean would choose what to air. And the Playboy Channel would only go so far with it's porn.

So, yes and no. If we allow vertical integration, then sure, content creators by the nature content creation choose what is or isn't appropriate in their eyes. Web hosting is another story, because they don't really create content, and there are so many sites it is almost impossible to censor.

I'd lean towards less censorship, wouldn't you? Freedom of speech is tough that way - sometimes we don't like the messages people see.