How was it transphobic? The whole entire show is extremely critical of the wars (Vietnam in theory, and Korea in practice), the military, and the state of society in general.

Stating that it's transphobic because it just depicts a common practice of draftees seeking non-dishonorable discharge is like stating "Get Out" is a racist movie because it depicts racism.

The only hate ever depicted towards Klinger is by characters that are considered antagonistic. Not to mention the multiple plotlines that are extremely supportive of homosexual characters.

Save for the first three seasons with Hawkeye and Trapper's overt "womanizing", it's an extremely woke show even by today's standards. Alda even spoke out against his character being written as such. At most, it's fairly misogynistic. I'm not really sure how you come up with transphobic though, unless you haven't really watched it.