For an outsider, it is difficult to fully appreciate how people might connect with a place based on faith.

It's not just about faith. It's about history as well. Let's not forget that non-Jews in the land were never forced out of their land. They could live next to Jews. But they didn't like Jewish authority over the land. They wanted another Islamic state, as if the other 20+ Islamic states in the world weren't enough for them.

What adds even more confusion is the position of the anti-Zionist Jews. Many of them being Orthodox. They claim Israel can only be regained miraculously.

The anti-Zionist Jews are a fringe. And how are they going to explain their own Bible which says if God scatters, no one can gather. When King Cyrus helped the Jews to go back into the land based on their Zionist request, about 2500 years ago, where was the miracle in that? How was that any different from what happened in 1948? And yet the Jewish Bible says it was God who did that and Cyrus was merely God's servant, doing the will of God.

There is also the issue of the Muslims connection to Jerusalem.

Muslims have Mecca as you said and Islam was founded in Arabia. Muhammad spent most of his life, if not all of it in Arabia. Not in the land of Israel. Furthermore, historically speaking Muhammed came about ~2000 years after Moses. If we really want to respect the order of history, we again have to give the Jewish people authority over that land, not the Muslims.