They shouldn't though as they aren't actually the ones taking the money, they're just a middleman. Anything that functions as a means of transferring money from one entity to another should be forced to not discriminate outside of legally mandated things such as sanctions/known criminal money and the like. Anything less just leads to this unpersoning bullshit we're seeing.
They must be granted the right of refusal. If only as a practicality. Just think about money laundering. That right of refusal is why it's so important that they are either strictly regulated (which I would say is probably sub-optimal) or not allowed to become a monopoly.
All money transfer services that i'm aware of have that right of refusal. And pretty much for that exact reason. It's a consumer protection in many cases.
Granted, the internet blurs some lines. I'd say those lines are being blurred because of the ubiquity of Patreon though. With competition, honestly, the entire issue goes away. I'd say competition is a more positive force than blunt administrative oversight (which will also be just as prone to this kind of political corruption, it will just be less transparent).
Edit: The more I think about it the more I think it might actually be a difference in perspective between American ideas of the market and European ideas of the market. Kind of another reason that there needs to be competition in these things rather than strict top down regulation. Competition will allow providers to find their market, which (I think) is what you want to happen. Regulation of speech through patreon funding (even well intentioned) will lead to an excessively divisive political argument which inhibits service of the individual (again, that's just my leaning). European socialism probably DOES function like that though. Well, we kinda know that it does in some areas. And it works sometimes too. American capitalism is not flawless itself. It's not a good/evil right/wrong sort of argument. But once you start linking people's ability to speak into it it'll inevitably become that. Which is, to my observation, exactly the issue that patreon is highlighting with their derp.
The competition aspect can't even be approached until the issue with Paypal being the only real game in town when it comes to easy online money transfers is addressed. Anyone looking to compete with patreon by pulling in the right leaning crowd is going to start handicapped by paypal inevitably telling them to get bent.
That aside, I still stand by my opinion. Any business that provides any service of any kind should not have the right to discriminate who they offer their services to outside of legally mandated reasons, and in-contact conflict with the entity seeking use of that service. This garbage with treating businesses as people needs to go. You're entering into societal realms with your business and need to act as a part of it, which includes providing your offered services to every single person within that society. I don't care if it's someone trying to censor nazis or not bake a gay wedding cake. The opposite of this is the "just start your own platform!" bullshit that completely abandons context and reason for ideological fanaticism.