> Why do payment processors do stuff like this? Is there some regulation that requires them to?

Generally no, but they exist in a regulatory morass where it's impossible to do what they do without arguably or perhaps technically being in violation of hundreds of regulations at any given time.

The US government then uses their power to selectively enforce the voluminous mess of bad regulations to coerce parties to undertake actions which it would be flatly illegal for the government to perform directly such as cutting off sexually explicit content from payment rails.

e.g. https://en.wikipedia.org/wiki/Operation_Choke_Point

The practice isn't limited to payment processors but they're a particularly good vector given the level of regulation they're subjected to. Choke Point (and Choke point 2) are just specific examples of a general tactic to end run around the public's rights that has been used by the US government for decades. In most cases the abuse isn't so well organized that it has a project name you can point at.

Congress and the whitehouse leaning on social media companies to suppress lawful opinions on covid policy is another example of that kind of abuse that has received some public scrutiny. Most cases, however, go without notice particularly since the ultimate victims of the actions generally have no way to know the cause.