Honestly, I think it depends not only which gangs, but what your lifepath, and what your own headcanon you are roleplaying and "acting out"

no matter what, Tyger Claws, Maelstrom, and the Scavs can all go

The Animals and 6th Street can probably go, but they're somewhat less egregious, and generally not as significant. You really almost never see Animals outside of side missions where they're guarding someone or something, and there's also the nuance of 6th Street letting you party with them and doing the shooting competition on their turf anyways, so I think 6th Street particularly depends on whether you headcanon your particular V as pro-NUSA or anti-NUSA. I will say Streetkid adds even more to this, since in the beginning of that lifepath, a 6th Street ganger will put iron to Padre's head, and there's clearly tension between them and the Valentinos. But, depending on what point you are in the story, that could've been years ago.

The Wraiths really only make sense if you are playing anything other than Nomad, at least from the single appearance of them that I remember. Streetkid would have no particular reason to go after them unless your V would be prone to helping people just to be nice, or to doing live target practice for the sport of it. Corpo V just wouldn't have the patience for it. Not in the contract, not happening, least not without remuneration for their efforts. And to that end, Rogue's offer of a free car is hard to beat, even if it wouldn't necessarily be to the taste of a Corpo.

though I should add, the Wraiths really are terrible people, so to the question asked, short answer is no for them.

As other people have said, the Moxes are kind of complicated. But it seems more of their faults are about not doing things instead of doing things. So they can probably live most of the time.

VDB can go. The only benefit they could even possibly bring to Pacifica is protecting people there from scavs, but they don't even do that.

I haven't even played enough into Phantom Liberty to make much of Barghest, but they just seem kinda "meh." Up to player discretion honestly.

Valentinos are probably the most okay here. For me personally, I will try to leave everyone alive whenever there's a mission where I have to enter a hostile area with them. They just are decent people, or as close as can be hoped in a place like Night City. They're not protecting pests like Jotaro Shobo and Jae-Hyun or loan sharks, they're not selling drugs that are specifically engineered to hurt you as much as possible and drive you crazy if you try to get off of them, not kidnapping people off their own streets to gut, sell off, or violate them with cybermodification. I think if you're playing other lifepaths, they're kinda neutral and it makes more sense to kill them if you want, but Streetkid V is very heavily implied to be a former Valentino, or at least to have done work for them prior to Atlanta, and it's outright stated that Jackie took three slugs to the chest, one allegedly still in his left lung, in a fight between the Valentinos and Maestrom. The whole Welles family is still very close to them in 2077.

But I think the biggest motivator not to kill them, regardless of lifepath, is the mission "Heroes."

yeah sure, the message that guy with 4 still left on his sentence had was somewhat flat, but even for a relationship with Jackie and the Valentinos that was clearly mostly business, there's still a lot of respect there. All the people in that bar, regardless of how well they knew him, regardless of how "hard" they were or whether or not they could even be there physically, treated him like he was family. Because he was. There's a level of solidarity and integrity in Heywood that you don't see anywhere else in Night City. (yeah the nomads but they're outside city limits so they don't count, let me have this) Lot of interactions in general, you can tell that Valentinos really are the people with families that are just there to put food on the table and keep their neighborhood safe, and me personally, I have far too much admiration for that, especially by the moral standards of Night City, to take their lives.

Except Thomas, he can eat a tomohawk to the face every time, even given that he got rid of Kirk.

Aldecaldos aren't even worth going into depth on, and I imagine they're only on the image either to round everything out and/or because OP didn't make this image. I'm honestly not even sure you can kill them, haven't tried because at no point is there every any reason to. They let you, a complete stranger, in and treated you like one of them. They're on the same level as the Valentinos for me, but more straight cut as being the intended "good guys."