The same "supermoral" Captain Arhcer who regularely is willing to risk his whole ship and crew for not harming anybody is boarding an Illyrian Vessel they befriended before, stole their warpcoil, leave them marooned for years in an enemy space (for the greater good)... and then after earth is saved, he is not going to look again for them
Maybe the Vulcans sent a ship after them. Maybe Columbia was sent to look for them. Maybe even the Xindi went looking for them after sending Enterprise home. Maybe they encountered an automated repair station on the way home and everything turned out okay. No one knows. They were an afterthought to the whole crew. And seemingly everyone else in the quadrant as they were never mentioned again.
The same captain who helps on the cowboy planet the now supressed former slaveholder race to emancipate in the now human dominated society, doesnt care at all about the destinies of hundred enslaved humanoids on the orion slave market as soon as he has his crew back.
It’s also known that Archer had an ancestor that fought in the Eugenics Wars. And that Augments have been described as being like Napolean, and associated with tens of millions of deaths. I don’t think Archer can be faulted in prioritizing Augments, since they could end up triggering a major interstellar war. And they just got out of one with the Xindi.
Plus, Enterprise is only one ship, and part of a fleet comprised of less than a dozen starships. You should really be asking what TF are the Vulcans doing, since they are the major interstellar power in this period. Yet they too are looking the other way when it comes to the Orions and their slave market.
He denies the asylum request on a humanoid who is only used as a breeding incubator, but enters uninvited the camp of an hunting party on their "game planet", being their guests, and then decided to help the prey of a hunting party not being because they appear for him like a girl he deems attractive.
Well first, it was the other way around. And T’Pol did question Archer’s decision making there.
Next, I'll start by saying that none of the Big Three are great with queer identity. Trip cannot conceive of a third gender or alternative lifestyles (which looks really bad from a mid-2020s perspective, WW3/post-atomic horror taken into consideration or not), and T’Pol uses the wrong pronoun in reference to the cogenitor. The only time we EVER hear proper pronouns used in the series for a different gender is from Hoshi in regard to the white sticky creature near the end of “Vox Sola”.
If looked at from Archer's perspective, Archer is trying to forge ties with a power that is at least three centuries ahead of them in technology. Which is important to him as someone who feels like humanity was held back by the Vulcans. Reed got Starfleet schematics for photonic torpedoes while wooing the Vissian tactical officer, which ended up being of great help by the time they were facing the Xindi. Who knows what else the Vissans would have shared if Trip did not mess things up? Granted, Archer should have pressed for more information from the Vissians about the cogenitors before coming to a decision. But it does not change the fact that Enterprise was outmatched and outclassed, and would have been overpowered by the Vissians in a firefight if they wanted to take the cogenitor back even if Archer did grant asylum.
It’s also nonsense that Trip did not think to consult Hoshi, or especially Travis (who’s seen and experienced things Trip hasn’t because he’s a space boomer), on a second opinion on what he was doing. Maybe if Trip had, and they opposed him, he might have reconsidered what he was doing. Frankly, he was let off easy by Archer.
But that's the point of the episode. That there is no easy answer.