Both the US and Israel support a (second) Palestinian state. They oppose the recent tactic the PA tried to use to get it.
The big demand was that the PA comply with international law and achieve peace and final status borders through peaceful negotiation as required under UN SC Res 242 instead of avoiding it. More detailed:
Hamas' charter is that Israel must be destroyed. All of it. And that Jews must be killed. All of them.
The PA may "recognize" that Israel exists in some of their statements. But, they also teach and preach that 100% of Israel must be destroyed and replaced with an Arab only Palestine. Their schoolbooks and official PA maps all show Palestine as including 100% of Israel and Israel does not exist on their maps.
2. More importantly,
Israel turned most of the West Bank and Gaza over to the PA.
Israel gave them money, weapons, training, buildings, and communications equipment.
The PA side responded with INCREASED incitement against and violence against Israel (often using those same weapons and communications equipment.
The PA violated their obligations from day one while Israel met hers for years and years, waiting and hoping for some reciprocity.
I think I can explain why many oppose statehood via the UN. (I don't think anyone or at least no majority is against their statehood in principle, it is about whether it is achieved through negotiation or via a UN vote)
Personally, I find my position changing. I do think it may go very very badly for them because an attack on Israel would be a full out act of war by a sovereign state and lead to a crushing response. But, if that is the route they want to go, maybe so be it. As a full sovereign state, naming your government buildings, high schools, little league teams and stadiums after those who kill civilians may get more press attention and put greater pressure on the PA.
For those that do oppose it, I think they oppose it for these reasons:
A) the UN has no authority to vote on this.
In 1948, the UN only had authority because the UK ruled that land. And the UK had the full authority to do as they wish and THEY gave the authority to the UN.
No one has such authority now, which brings us to B.
B) According to International Law and UN SC Res 242, the land in question does not belong to Israel NOR does it belong to a state of Palestine Nor does it belong to anyone else.
Under UN SC Res 242, the land in question is in legal limbo and belongs to no state UNTIL and unless all relevant parties peacefully negotiate final status borders. Until then it may be administered by Israel.
And the Arab side has rejected peaceful negotiation or violated every obligation negotiated. So, providing a new state through any other means is illegal under international law.
C) In fact, the entire vote constitutes an "end run" around the law.
Instead of seeking peace and negotiating final status borders AND recognizing Israel's right to exist safely AND not attacking Israel, they teach and preach that 100% of Israel must be destroyed, they incite violence and attack Israel, they get as much land as possible through negotiation and violate all of their obligations under the treaty and then they unilaterally seek the rest of what they want through a UN vote.
It actually sounds eerily like Arafat's 1975 "Phased plan for Israel's destruction" which called for negotiating peace treaties to get as much land as possible and then violating the agreements and using all land won through negotiation as a launching pad for destroying Israel once and for all. And both Arafat and other PA ministers have repeatedly said (since Olso) that this plan is still in effect.
And it rewards bad behavior.
D) Finally, the current political situation is untenable. The PA and Hamas have split the area and generally kill or torture or maim one another's supporters. Would a vote mean 2 warring Palestinian States or One Palestinian State ripe for civil war?
PS: the settlements are not on "stolen lands." They are on land that is private property owned by Jews (but who were ethnically cleansed in 1948) or on government owned land. The land is not "stolen." It is land that the Palestinian Authority and Hamas WANT to be part of their state. But, there is no legal basis for this. In fact, under international law the land "belongs" to NO state. That is why UN SC Res requires all relevant parties to peacefully negotiate where the borders are.