There are differences of opinion in rabbinical circles. Everyone holds that one cannot enter the holy of holies, but that is on the large rock presently occupied by a mosque with a golden dome, so it’s pretty easy to avoid.
I thought there were disagreements as to where the holy of holies had been placed, so it was safer to avoid going to the Temple Mount altogether. Mind you, I still place 99.99% of the fault with the Muslims, but I would feel better if the Jews were united defending their right to that holy place.