The market hasn't failed, it's perfectly possible to sell adult content online, it's just relatively more expensive.
"From the outside, it looks like this is a market failure that has no reason to exist other than institutional bias that is no longer grounded in reality."
I think you're being a bit naive there. Surely those companies would have no objection to tasteful nudity or educational content, but if you want to process actual porn you'll have accept a lot of seriously offensive content that you definitely don't want to directly associate with your brand.
We have a situation where people are are trading money in exchange for goods. Presumably, this is happening because the people spending money value the goods more than the money; and the people selling the goods value the money more than the effort to produce the goods [0]. This means that these trades not happening is, by definition, an inefficiency. By definition, a situation causing an economic inefficiency is a market failure. Unless you are arguing that every transaction Patreon is now blocking will still occur without Patreon, then Patreons decision is causing (or, rather, worsening) a market failure.
Creating an entirely efficient market is a hard problem, so the existence of market failures should not be surprising. But, when we see a clear example of a market failure being introduced, we should question what is the reason, and if there is a way we can avoid it.
[0] Even after the 5% fees Patreon charges. There are also cases where the transaction is not entirely quid-pro-quo (eg. people donating to support the creation of free content), which mucks up the Econ 101 analysis, but I don't think effects the broader point.
It's actually an example of the market mechanism solving the problem, you're just ignoring a few actors here:
The payment processor of Patreon has an interest not to deal with the porn, therefore declines the business.
The payment processor of competing actual porn platforms has a market niche to take exactly that business.
All the middlemen that are required here (for complex reasons) get paid for making it happen.
Nothing is lost, therefore no inefficiency, therefore no failure. The money not spent on one performer through Patreon can instead be spent on any other performer wise enough not to rely on Patreon for payment.
"From the outside, it looks like this is a market failure that has no reason to exist other than institutional bias that is no longer grounded in reality."
I think you're being a bit naive there. Surely those companies would have no objection to tasteful nudity or educational content, but if you want to process actual porn you'll have accept a lot of seriously offensive content that you definitely don't want to directly associate with your brand.