That's less for ideological grounds and entirely to do with the chargebacks that ensue when the wife finds the bill and the husband denies everything, insisting the card was stolen, and the shitty business models of shady outfits opting you into recurring subscriptions that require your using a credit card as "age verification." All of it gets contested and it's more trouble than it's worth.

American Express explicitly bans porn outright. It's not for some prudish reasons though, it's because porn has a very high fraud/chargeback rate.