Payment processors have never been classed as even kind of a common carrier. Pretty much the moment you deal with money the government will more or less be your "partner".

Cloudflare notably has not been legally forced to take the positions it has. You can be a common carrier as much as you want

Regarding the money sensitivity issue, I do understand KYC, etc. However, once they determine that you are not doing anything illegal, they are simply moving money from one person to another and in that respect that are a "kind" of common carrier. Porn is not illegal. So they are specifically stepping in and making a socially acceptable (to them) judgement call to stop something that is perfectly legal when they should be just making sure you are not a terrorist or drug-dealer and minding their own business.

>Cloudflare notably has not been legally forced to take the positions it has.

True they flip-flop depending on how the winds of Twitter are blowing, but they are quickly positioning themselves in such a way that someone could earnestly claim there is not reasonable alternative and that they are "required" to run a business. Then what?