Trump is going to compromise our country's relationship with most of the world, not just Israel. He has no idea how diplomacy works, and knows nothing about foreign relations and affairs. He is just going to run his mouth, causing other nations to turn against us and possibly creating a huge mess.
Most of the pertinent communications with Israel are being channeled through the CIA and it appears that Trump is going to have an adversarial relationship with his own spy agency. Additionally, Trump likes to boast and opine very publicly and in so doing, tends to upset many parties that he didn't even consider sending his tweets.
Donald Trump has not even been sworn in yet so we have cannot predict how he will handle the state of affairs with Israel. Trump's son-in-law is Jewish and it has been reported that he will take an active role in relations with Israel. For now, Americans will just have to wait and see how things unfold.
No, Donald Trump will not compromise our relationship with Israel. Donald Trump is a shill for Israel and will continue the tradition of American politicians selling out and endangering the American public in order to provide benefit to the state of Israel and the lobbyists that work in its interest.