Trip did strike me as "Broken Bow"-naive in "Cogenitor." Remember in "BB" when he sees that child fighting to breathe, and he automatically assumes the mother is abusing him and is ready to go over there and save the kid...but it turns out he's dead wrong? "Cogenitor" had that same vibe. Except Trip blows off T'Pol's caution ("It's not our place to judge the customs of other cultures"), as well as Phlox's caution ("It's not a question of right or wrong"). Even the cogenitor tries to stop Trip when he brings that book to it, unbidden, and tells it about all the rights it's entitled to (oh yeah, if it were human, which it isn't). Its response is, "It's wrong for me to read"..."You shouldn't be here"..."That may be true on your world, but not on mine"..."You don't understand."
For a guy who had the maturity to command effectively during "Cease Fire" and keep the Vulcans and Andorians from starting a war right then and there, such bull-headed denseness does seem out of character to me.

I think the point being made was that Trip was still prone to being impulsive and not considering the consequences of his actions. But it was still a step backwards for the character Trip had become.
It would have been great to know what led to the subjugation of the cogenitors on Vissia. Some past medical disaster in which the ability to reproduce was almost lost? A failed attempt by the cogenitors to take over the government? We don't know. But it didn't matter for the purposes of the story. The Vissians were treating the cogenitor correctly from their POV, and Trip believed they were wrong.
I disagree that Trip's behavior cost the humans the "moral high ground." The test of a just civilization is in how it treats its weakest members. In my view, the Vissians were the inferior society.
Whether they were or not, that didn't give Trip the right to pass judgment on them, using human standards of morality, without even bothering to learn anything about their history or culture.
And I disagree that Trip was "going behind everybody's back."
Well... he went to the Vissian couple's quarters to teach the cogenitor to read, after telling the engineer he was going to the mess hall for lunch. During a later reading session, Trip tells the cogenitor "they think I'm in Astrometrics." And when he sneaks it aboard
Enterprise, putting it at risk of punishment, he says that they'll have to make sure no one spots them.
Archer's record up to "Cogenitor":
Every discussion about "Cogenitor" seems to turn into an Archer bashfest sooner or later.

He wasn't even on
Enterprise for most of the show. To me, this story is about Trip, and a dilemma with no clear "correct" solution.
Of course, in Season 1 (four of your five examples), Archer had a tendency to barrel in when he saw someone needing assistance. From the looks of "Dear Doctor," he was really struggling with the issue of non-interference, since there was no Prime Directive yet. I thought it was cool to show that, once upon a time, starship captains had to wing it, and official guidelines were needed. Never mind that Trek is famous for ditching the Prime Directive whenever needed.

"A Taste of Armageddon" and "The Apple" come immediately to mind.
I could totally buy that Archer's impulsiveness had waned by late Season 2, in favor of weighing the issue of doing what he thought was right vs. interfering with other species, as he put it. That shift toward a more objective, "prime directive" attitude would seem to be a logical and necessary step for a maturing commander.
Watching this episode was really uncomfortable and sad for me, because I like Trip, and he seemed written to be all heart and no brains in this one. The ending was tragic. But if the cogenitor had been granted asylum, that would have been a tragedy for the Vissian couple, and countless other couples.
lceb has a point: the cogenitor's death might have compelled the Vissians to re-examine their long-held views, just as the deaths of Romeo and Juliet were a wake-up call to the feuding Montagues and Capulets.