Two things make that exchange a bit of a different equation.
The first is that it's private correspondence. Running into the court and yelling 'Queen so-and-so was vulgar to me in a letter' is likely to make you look just as ill-mannered for sharing private correspondence - and if it didn't (because everybody hated the author, for instance) then they probably already think so poorly of her that vulgarity isn't going to add to the shame of it.
The second is that there is a religious zealotry element at work, and medievals can and did make an exception to normal rules when it came to treating with infidels. We get away from this in BM because we have lots of religions and we mostly tolerate them, as opposed to few religions (but many heresies) and very little tolerance going on. One Turkish Sultan famously used a Byzantine Emperor as a footstool. Calling names would seem a bit trivial at that point.
I would still answer the question of 'are these letters vulgar' with a definite 'yes' because of both the graphic threats and the bedroom talk, but given the context of rivalry in private correspondence, I would probably click on 'not vulgar' if it had popped up with the question.
