Why do credit cards care about what the money is paying for? Are they just more moralistic than banks?
While that's possible, there's a more realistic solution. Credit cards companies don't care about what you buy; they care about chargebacks: customers calling to say that such and such a charge was made fraudulently, or for some other reason should be undone.
I believe this activity tends to be heavier for adult sites than elsewhere, and possibly for some types of adult content than others. There are a number of reasons for this: shame and embarrassment over having indulged; fear of significant others discovering the charges; significant others actually discovering the charges; someone actually charging to a card without the cardholder's knowledge (from waiters to your kids). In any case, it's a hassle; it costs the companies money (for the charges reversed) and time (and employee time, for people handling those phone calls, translates directly into money as well).
I'm not entirely sure that going with banks directly would resolve all of this. At least some of the hassle the credit card company is dealing with would devolve on the banks. Something tells me banks might have a lower threshold for putting up with this; there may be a termination clause in the ACH contract that would relate to this.
Pretty sure they're just being morality police (which kinda goes against the sole purpose of a corporation, to max profit, nothing more, nothing less), otherwise why distinguish vanilla porn from rape, incest, beastiality, etc types they don't like (and I find it especially weird that actors portraying step-relatives fucking is apparently fine, but portraying blood relatives is not, when in alot of places both are legally incest, that's been the case since the late 1980's before porn was on the internet). Why not just ban all porn? AFAIK they've never given a public statement telling their logic or reasoning and there's nothing in legal agreements detailing why either, other than basically "anything we feel like, for any reason or no reason, since it's our way or the highway since we are essentially gods that can do things even the gov't can't legally do". But CC's don't have to honor chargebacks, sometimes they will, sometimes they will just tell you "tough luck, too bad, buyer's remorse is not a legit reason if it can't be physically returned", unless you have proof it wasn't you that charged it (difficult even when that's the actual case, often requiring things like copies of police reports if the CC was supposedly stolen and not part of a database breach). With ACH there is no charging back AFAIK, once the account is pinged for transfer there is no changing your mind or undoing it once it starts (the bank isn't liable, the account holder is, unless theft/fraud can be proven and then gets the FDIC/FBI involved). It's why many banks will refuse to link with Paypal, too many people were calling their bank and complaining once their Paypal was compromised and used to empty their linked accounts (dunno if that still happens, haven't used Paypal since early 2010's) or simply mistakenly using the wrong account/fund source when buying something (ie accidentally overdrawing the bank account and then getting slapped with a $40 fee).