Israel says the vote makes peace harder to achieve. But it's hard to see how membership in UNESCO (which coordinates educational exchanges, certifies "World Heritage Sites," and is generally the UN's culture wing) makes peace less possible. The vote reflects the broad views of the UN's member states: That it's time for a country called "Palestine" to be admitted as a member to the UN.
It doesn't give the Palestinian Authority sovereignty over the West Bank, change the position of Israel's settlements there, or upend the status quo in East Jerusalem. The Palestinian argument in favor of its overall push for recognition at the UN (a vote on that issue is currently stalled) is that it will galvanize Israeli politicians into working harder for a peace deal, since it's evidence the Israeli government's position is losing international support.
The real argument for a two-state solution (whether you accept it or not) is that Israel's ongoing control of the West Bank leaves it as the de facto sovereign over millions of Palestinians without voting rights in Israel, or a state of their own. In the long run, that confronts Israel with the choice of giving Palestinians full citizenship and the vote (not likely, since that would be the beginning of the end of the Jewish state given far higher Palestinian birth rates), developing an apartheid-style system where Israeli settlers live in the West Bank as citizens while Palestinians have a second, weaker position under Israeli law; or actually reach a deal.
The ground truth of those realities and choices doesn't change in response to what UNESCO does or doesn't do, nor does the range of possible choices Palestinians could make in the coming years. Another intifada, with terror attacks inside Israel? Large-scale, peaceful civil disobedience? An international delegitimization campaign to paint Israel as a modern version of white South Africa? All are possible courses a current or future Palestinian leadership could pursue.