What the US has argued historically is that American people and institutions are not subject to it because the US has a functioning civilian and military justice system, and so prosecution for such crimes can be handled within it, even by foreign nations and NGOs.
Obviously that’s a load of bullshit, especially (but not only) these days, but “sovereignty for me but not for thee” has long been the rule and with its weakening international position the US may come to find that to be less achievable in the future.
Compared to how much of a mess most of the world's powers are on matters on sovereignty, the US is actually one of the more conservative ones here (e.g., see OFCOM in the UK).
Let me restate: The US position is that the US justice system “works” and thus *US persons and institutions* must be pursued *within the US system* even by foreign entities.
In other words, the US position is not that if (say) North Korea commits a crime against humanity they must be pursued in US courts; the US is fine with the ICC in that case. The US position is that if the US commits a crime against humanity that must be pursued in US courts, not the ICC.
It’s an obvious (and bullshit) double standard, but it’s also not a denial of the legitimacy of universal jurisdiction. It’s just the US, as usual, trying to have its cake and eat it too.
That this standard is complicated, and different from those that argue that international law should be the supreme law, doesn't make it a double standard. It's also not what is meant by universal jurisdiction, as it does not depend on overriding sovereignty.
Edit: Seeing your other comment, it's also worth noting this was a large reason why the US didn't sign the Rome statute, since as you note, the US isn't inherently opposed to the idea of international courts, only the supremacy of their jurisdiction.
On the other hand, the US didn’t try to prevent Slobodan Milošević from being tried at The Hague for war crimes and genocide, as Serbia wasn’t a vassal state or proxy.
Anybody can look into any country’s actions unless that country has authority over them and forbids it.
4 State immunity evolved in close connection to the development of the concept of sovereignty
and the territorial State. It can be traced back to the principle of par in parem non habet
imperium which was mentioned as early as 1354 by Bartolus de Saxoferrato in his Tractatus de
regimine civitatis. It stipulates that a sovereign should not have jurisdiction over another
sovereign.
[...]
22 State immunity entails that a State itself or its property is not subjected to the
proceedings of the court of another State. It does foreclose any proceedings or judgment on the
merits, but does not hinder the service of process and a court decision about the admissibility.
Likewise, it protects the property of a State against any measure taken in relation to the
proceedings.
Many others have already pointed out the fact here - that Palestine is under ICC jurisdiction.
Instead what I want to focus on is WHY YOU DID NOT KNOW THIS, despite the fact that the ICC literally ruled on this matter quite a while ago, specifically. The court itself approached this question, evaluated the evidence, and made a ruling. You missed all that?