This is definitely a plausible Hank moment, but only after a long episode of him misunderstanding and getting it ignorantly (but not maliciously) wrong at first, being distressed and confused about how he’s out of touch with the kids and gender ain’t simple like it used to be
right up until some rude asshole does this in his face and he needs to stand up for his friends / family and suddenly Understands the emotional crux of the issue
“And you have all these so called whistleblowers claiming the government is putting chemicals in vaccines and food to make you one of them transgenders or homosexuals. But I’ve never seen a transgender support the government or one of those so-called “gay frogs”, so it makes you wonder what THEYRE really putting in this stuff. All I’m saying is that Chelsea Manning went to prison and Mr. Rogan is a millionaire, and you always gotta follow the money”
“Tell you what man, talkin’ ‘bout dang ‘ol critical gender theory man, ‘s all a construct, talkin’ ‘bout man’s man and real woman but I tell you what man, talkin’ ‘bout when the lights are off we all just dang ‘ol people man”
“Well I think she’s a real classy lady.”
Not to be that guy but this is already canon. At the beginning of an episode Hank refers to a trans bank teller as “in between genders” but after a whole ordeal of him accidentally receiving a driver’s licence that says he’s female and everyone treating him like a woman for pretty much a whole episode, he approaches the bank teller once again and refers to her as “ma'am”
Hank Hill is canonically a trans ally after being misgensered himself
