Perhaps you are not legally obliged to give a reason, but it would definitely make you look a lot better then simply saying "uhuh, not here buddy".
I think you can't have it both ways, ignoring support questions and not having to deal with backlash like this.
For example, Stripe also prohibits adult content which is largely (I would guess) a result of input from Wells Fargo https://stripe.com/us/prohibited-businesses
It's still unclear to me why, if you have multiple banking partners, you don't have even one that would support an adult business. There is a lot of adult video and website business - they must have banks.
Furthermore, it's really the lack of transparency that rubs people the wrong way. When your customers are told that their accounts are frozen or closed all of a sudden and with almost no explanation, they are left flailing to try to understand what the heck is going on. It's like being kicked out of a restaurant half way through dinner and when you ask why, they just say "sorry, we can't continue to serve you..." I consider that method of dealing with your honest customers disrespectful.