I never found Klinger offensive. It started off on the premise that you had to be crazy to put on a dress, but everyone just acted like he was Klinger. He was never meant to be trans, it was supposed to be a kind of Catch-22 situation in the totality. And then he developed a love of the clothing. And he was accepted by a lot of the women (especially the nurses under Margaret who saw them as "one of them.")

There's an episode where he stops wearing the clothing and he develops a rash. The doctors couldn't identify the cause so they call in the shrink, Sydney Freeman, who basically says, "Sorry Klinger, this is protective armour for you. The clothes are now part of your life, and your barrier against the bigger 'insanity' that is the army and war." With the broad point that a man wearing a dress (translate it to trans people today) is 100% normal in any comparison to a nation invading a country and murdering tens of thousands of people.

MASH was counter-culture, the film certainly was. It was toned down for TV, but it still and often took the progressive, humanising view on things. Trans people weren't as "out" as we are now. It's definitely of its time, but broadly, with everyone taking the view that Klinger was a normal, valuable human, whatever he wore, I'd say it's an overall success.

Although now I'm thinking of an actual TG Fan-Fiction MASH where a Klinger-like character uses a Klinger style approach to getting out of the army as a "cover" for transitioning in the army. Maybe the army, as it's a MASH hospital, against "army" rules decide to let "him" keep going. Offering against-military-rules such as HRT, then surgeries, etc. to see how serious "he" is, with no-one actually saying the words "I'm trans"/"We know you're trans." It is "Don't Ask/Don't Tell." In the end, and the slow burn of it, is everyone knows the Klinger-like is trans, and they just want the military to pay for her transition, which otherwise would be unaffordable. (With lots of hijinks such as very officious Generals coming onto her. I can already see an episode where an investigator comes to the base as they hear the doctors are refusing to discharge a "man-in-a-dress" and he singles out every woman as "the-man-in-a-dress but the Klinger-like, who he immediately clocks as too beautiful to be a man, and enlists her to help him.)