As I have said elsewhere, I can only speak with certainty on VMI. But from my interactions with my counterparts at other military schools, yes. Profanity (and other vulgarities) are pervasive.
At the end of the day, all military schools are products of society, even if we're 10-20 years behind. I was recently talking with an Alum from the Class of 1980. He distinctly remembers a situation in the late '70s where some of the Cadre were swearing at rats in ranks (outside barracks), and some Alum overheard. They pulled the Cadre members aside and lit them up, and then sent them up to the GC (recommended them for a penalty from the cadet government). Today, it would be impossible to enforce this kind of standard. And to be honest, it takes a while for people to change their vocabularies after they've been talking that way throughout high school and before.
That said, we do try to keep an eye on Cadre and other cadet leaders. There are penalties for excessive use of profanity when training/correcting the rats. But when they're with their buddies? They can talk however they want to, behind closed doors.
Another dynamic to remember about VMI and The Citadel is that they're almost-all-male schools. Women are still so small of a minority that the guys often forget we're around. It leads to some pretty funny (and embarassing, though usually more so for the guys) situations. It's just like any other time you get a bunch of college aged guys together, though. It's locker room talk, only the entire barracks is the locker room.
It can be difficult to maintain your personal standards in accordance with religious convictions in this kind of environment, but there are always others around. I know at VMI, Chaplain Park provides several opportunities a week for cadets of all faiths to get together and encourage others within their faith group. I'm sure The Citadel has similar religious services available. It's a lot easier as an upperclassman, too, when you can choose your own roommates (I assume it's the same at The Citadel).
As a female cadet and as a Christian, I strive hard not to use foul language or tell dirty jokes, but I'll be the first to admit I'm only human.
The guys I hang out with know the limits, though. I'm very hard to offend, so when I do speak up about something being inappropriate, they listen and respect those limits. I have no reason to believe that cadets at other military schools would not show the same level of decency. And if they don't, well, it will quickly become clear to your son/daughter that he/she should find a different crowd to run with. It's all part of the process of striking out on your own for the first time, truly owning your faith/value system, and being forced to take responsibility for your own decisions regarding your lifestyle and social habits.
Hope this helps.
Jackie M. Briski
VMI Class of 2009
Cadet Chaplain