The Palestinian objection to US recognition of Jerusalem as the capital of Israel is that they want Jerusalem for the capital of their state following an eventual peace agreement. But Jerusalem will remain the capital of Israel as well after an eventual peace settlement. So what is the harm to the Palestinians of the US recognizing that fact?
In 1947 the UN offered two states for two peoples. The Jews accepted and created a Hebrew Republic with Jerusalem as its capital. The Palestinians refused and have neither state nor capital.
For 70 years they have endlessly demanded a state, and just as endlessly refused one when the condition for it was peace with Israel. Now, they grudgingly might, just might, accept a state someday in the future.
Again, how does preparation for a state the Palestinians have repeatedly refused to have, preclude recognition of the capital of a state the Jews have long since accepted and established?
How does their objection make any sense?