Aspects of her treatment were misogynistic (the shower business especially) and it would have been more convincing if she resigned or at least demanded a transfer to another unit. I too find the character change unconvincing.
"Chicken soup - with a beep straw."

Good explanation. Pointing out that her change wasn't as abrupt as it seemed at first
glance.

Wow, I'm really surprised no one gets this character change. It all seemed very clear to me when I first saw it that without the influence of someone like Major Burns, and with increasing familiarity with the "cool" people, she would free herself up to be what she always secretly wanted to be: one of the crowd. She's like the Catholic school girl who gets out in the world and discovers that there's fun to be had. With no one else around her to reinforce her old uptight ways, she found that she just wanted to have fun like everyone else. There were even fore-shadowing events in the film that demonstrated this change. For instance, when she is praised by Hawkeye for being a pain-in-the-ass but a "damn fine nurse", you could see her delight at the compliment. Then there were scenes of her hanging out with the boys during their poker games (I admit it's been a while since I saw the film), so she was already starting to chill out a bit. By the time of the football game, she was fully on board with the gang. There was nothing unusual about this at all. Remember, also, that the film was a thinly disguised commentary on the Vietnam war, and there were a great many people in the '60s who were gung-ho for the war only to realize that it was wrong and eventually joined the majority of people who opposed it. The Hotlips character perfectly symbolizes that type of person.

Altman seemed to have a slippery sense of what his lead female character was about. It's noted on the Goofs page that she's alternately referred to as Major Houlihan and Major O'Houlihan, the later of which may be Col. Blake's mistake alone but one which she doesn't correct him on. In regard to her scenes in the football game, she's completely different from the strict, bristly character we got to know before. I don't think it's implied that sex with Duke gave her a new perspective.
I think a lot of "MASH" got lost on the cutting-room floor. They were working without a script, as they famously chucked the dialogue Ring Lardner gave them. In that event, it's not hard to imagine them losing character identities and personalities as the filming went on. Definitely a flaw to me.

The more I think about this, the more I think the change is actually in line with her character, at least in one respect: she starts out as a "cheerleader" for the Army, rigidly enforcing protocol, which irritates the anti-authority characters. But after she realizes that Hawkeye and Trapper are doing whatever they want without repercussions, it must seem to her like they are the ones running the show. So Hot Lips decides to become their "cheerleader" (figuratively and literally) since she's a follower of whomever is in control. The whole thing makes Army authority seem like even more of a joke and shows that the subversive characters have taken over.

I think she just finally accepted the fact that she couldn't change the 4077th, so she joined in with the shenanigans.

You're absolutely RIGHT ~ I thought the SAME thing!
And I also thought {and noted elsewhere on this message board} that the whole 'football game part' of the film was not only out of the film's "character", but not funny and a complete waste of time.
'You can't HANDLE the truth!'

I think this was to show her character change over time. We can assume Duke and Hawkeye get there fairly early in the war and leave when it's almost over. That could be enough time for Hot Lips to have a change of attitude.

It's a combination of her awareness that Col. Blake had no intention of disciplining Hawkeye and Trapper, and that word had reached her that General Hammond, to whom she and Frank had sent a letter of concern about how the camp was run, was so keen on football(and that he'd dropped his inquiry re her claim) that she figured she'd get on board with her support.

I figured she thought "if you can't beat them, join them". Sure, it was pretty overdone. For comical relief.

This part bothered me the most, she was abused, bullied and humiliated but at the end, she chose to act like a stereotypical dumb blonde girl. And I guess just because it's Altman, we must give the film the benefit of doubt and consider that it was a gutsy movie that makes it a "fearlessly inventive director" I don't know. I guess it was just written by a guy who wanted the strict woman to be 'domesticated', who wanted the bullies to win, like a mean-spirited version of Benny Hill.
"Darth Vader is
scary and I
The God
father"

It was an echo of the sexual revolution of the '60s. After hooking up with Duke she was supposedly liberated and able to cast off all the old straight-laced morals of her military upbringing, which reflected the morals of pre-60s America. That was after all how Hawkeye and Trapper lived. In the 2010 time frame it all looks a little dated and ridiculous.
That was one thing about the series which was much better than the movie. Hot Lips in the series gradually became a much more liberated woman who did not depend on any man and who became much more comfortable with herself. Supposedly this happened because Loretta Swit was unhappy with the original one-dimensional aspect of her role (which caused Larry Linville to leave).

"Scorsese could have suddenly transformed Travis Bickle into a glib, sociable man-about-town 3/4 of the way through Taxi Driver".
He could have - if it made sense and jibed with the film`s themes & purpose.
"facts are stupid things" - Ronald Reagan

But Travis Bickle is the protagonist. We experience the film through his eyes. Hot Lips, if anything, acts as an antagonist. We are not meant to identify with her. Perhaps we feel pity, but never empathy.

In my opinion, jarring, unexplained shifts in character are all part of Altman's brilliance
Well that's certainly putting a positive spin on things. Too bad other directors didn't pick up on this technique. Scorcese could have suddenly transformed Travis Bickle into a glib, sociable man-about-town 3/4 of the way through
Taxi Driver
.
"I don't want any Commies in my car. No Christians, either."

I think Hot Lips only wants to be accepted at this point. She is willingly ignorant, as long as they know she is on the team. Like an abused dog.
In my opinion, jarring, unexplained shifts in character are all part of Altman's brilliance. The shift temporarily stuns, and then forces us to ask questions: Depth.

You merely repeated my post, but with fancier words.

Three words: fearlessly innovative director.

All in opinion, my friend.

Two words: bad director.

How did I talk down to you, I am sorry if I offended you.

Thanks, avario. It's been a while since I've been talked down to like that!
"My brain rebelled, and insisted on applying logic where it was not welcome."

As an avid follow of Sally Kellerman, I am here to tell you all something: What a lot of you may not know is that when 'Hot Lips' walked into the commanders tent, she threatened to resign her commission. That line was said to not have originally been in the script. It was actually, Kellerman's own anger speaking out. If 'Hot Lips' resigned her commision she would no longer be in the film. So, Kellerman turned the role upside down and had fun, instead of being disgusted with what went on with her character.

I'm with you. That's the only thing that made me scratch my head.