In the US, that would be title II of the 1964 civil rights act, taking the broad view of it that has developed in case law over the years. I would also support new FCC net neutrality style regulations or even new acts of Congress that strengthened this.
Any changes to include internet services under the Civil Rights act would likely run into a First Amendment challenge fairly quickly, and likely lose. Net neutrality was probably constitutional as long as it applied to physical carriers using public land (for wires) or regulated spectrum. A more likely path would be through Section 508 (the accessibility act). Even that is unlikely with the current partisan makeup of Congress and the US Supreme Court.
I agree that there would be a better chance for this line of reasoning if Manhattan Community Access had gone the other way in the latest SCOTUS term. But it was 5-4, and the decision does leave open some lines of attack.
In particular, Congressional action around this might probably be able to pass judicial review if it were to define broad due process rights around speech censorship for explicitly defined "public forums." The only thing that SCOTUS loves more than the 1st amendment is the 14th.
