It's illegal activity in basically fraud. Adult oriented things have, unfortunately, a higher risk of fraud. Either true credit card fraud where people use someone else's card without authorization, or fraud in where they consume the content, but then deny it later on.
That's the illegal activity they care about because chargebacks and such are bad.
Buying gift cards, well, there's a legitimate case for that, and if you're being scammed to pay your taxes with iTunes gift cards, that's a matter between you and the scammer - Visa and MasterCard are innocent third parties. Since the fraud doesn't involve them they don't care.
But when it does involve them, like with adult purchases, then they care a lot.
Adult oriented businesses selling adult oriented things like content put up with much higher rates because of it. And likely both Visa and MasterCard offered Itch and Valve the same deal - either accept the higher rates since you sell adult oriented content, or don't sell adult oriented content.
Itch can restore the free content because they aren't selling or dealing with purchases. And as long as adult oriented content isn't purchased using Visa or MasterCard, well, they can't get involved.
(They could take say, Bitcoin, but most likely their payment processor might have an objection. Chances are though, the solution is to simply make a subsidiary business like "Itch for Adults" that can sell those content, with the caveat that they payment developers get will be lower as the fees are higher.)