I was in the U.S. Army.
Brutal initiation rites: Well, Basic Training was pretty grueling for me, physically and psychologically, but I don’t think it was brutal.
Confessing your darkest secrets to the training group: Nothing even remotely close to this. I’ve never even heard of this happening in real life.
A demanding re-birth qualification hurdle: I mean, sort of? In a sense, Initial Entry Training is one long re-birth process, to make you into a Soldier, but I don’t think that’s really the same thing.
Learning that your life depends on the team: Yes, absolutely, this part is definitely central to just about any military indoctrination.
Looking at the classic cult traits upthread, though, and military forces to tick some boxes, but not others.
The modern U.S. military is institutionalized and bureaucratized almost to the point of self-parody (many would seriously argue it is past that point). It’s about as opposite of a single charismatic leader as one can get.
Sexual abuse does happen in the U.S. military, all too often, but it’s not a core element of it. Sexual abuse as a core element are often attributed to historical military forces and many guerrilla forces, but it’s far from universal, and at least some of those stories are most likely of “that other tribe down the river are the cannibals” variety.
Also, and this is I think a really key point, the modern U.S. military does not try to isolate service members. It does make it hard to have a normal family life, but the leadership generally tries to encourage and facilitate family ties and involvement in the community, which is the opposite of cult behavior.
And you can definitely get out. Enlisted have contracts, but at the end of the contract, if you don’t want to re-up, you just don’t, and you’re free to go. For officers, it isn’t in practical terms as easy as just saying “I resign my commission”, but it’s not all that much more difficult.