>No, I'm saying that operating a site inherently involves that, and that they have the right to choose how to do so, even when that excludes certain views from their site, and that that right is enshrined in the First Amendment.

And I'm saying that no, it is not enshrined in the First Amendment. There is significant legislative regulation that applies to publishers and not to web hosts because they could not possibly regulate content on an individual basis.

That's why your second point is incorrect - if you read the legal decisions that have upheld the Communications Decency Act's Safe Harbor provisions, they aren't based on the collateral economic development cost or big money interests - they are based on the idea that it is an impossible task to regulate obscene speech online and that in order to do so, sites would have to chill speech. This chilling of speech (which is kinda what we're talking about here) is the reason sites are not treated as publishers, with again, the underpinning being that it would be impossible for them to regulate content.

If you are correct that they can do so and inherently do so, then the protections they are provided by not being held responsible, legally, as publishers, for the content they publish, should be stripped from them and websites and host should be treated as publishers, with all the regulations that apply therein.