These other guys have given a good gist of the issue, but IMO it’s inaccurate. The problem lies with society and capitalism at the end of the day. Basically, credit processors are in it for the money, obviously. And they view porn as a risk to profits, because puritanical society means that statistically a lot of sex related purchases lead to charge backs when someone finds out and the purchaser denies having any knowledge of it. So as a result the credit processors don’t allow their services to be used for sex stuff.

This is not to say that the credit processors AREN’T led by puritans with an agenda. Just that their profit motive probably has more to do with it.