The US’s decision to leave UNESCO is because of the UNESCO World Heritage Committee’s decision to inscribe the site of Hebron/Al-Khalil Old Town in the West Bank as a World Heritage site.
The key issue with many US-UN disputes is the Israeli-Palestinian conflict. In October 2011, UNESCO admitted the Palestinian territories to the organization as an independent member-state called Palestine.
This triggered a US law which cut off American funding for any organization that recognized an independent Palestine. The US had previously paid for 22 percent ($80 million) of UNESCO’s annual budget.
In 2013, after the US missed several rounds of payments to UNESCO, the organization suspended US voting rights in its core decision-making bodies. So the US hasn’t been a real UNESCO member for a while.