“What is terrible is for Jews to try to outlaw the free worship and practice of religions other than Judaism in Jerusalem”
Huh? You can be any religion you want, or no religion, in Israel. My country is the only country in the ME that permits that.
This concerns a property that is owned by (what translates as) the Jewish Antiquity Organization (not exact translation), a quasi-governmental organization under the authority of the Orthodox Rabbinate, put in charge of Jewish sites, such as this, the Tomb of David.
Permitting religious ceremonies of another religion is a very difficult issue.
Be like muslims doing whatever muslims do in the Vatican.
First of all, Catholics consider Judaism "a central component of Christian salvation", and refer to Abraham as "the Father of our faith" in every Mass. Catholics also seek to obey the "Ten Commandments" as delivered by Moses from God, and they hold David in very high esteem, and a portion of one of the Psalms (many attributed to David) are read in most Catholic Masses, and various other different Psalms are read several times a day by all Catholic priests, deacons, and consecrated religious men and women (monks, brothers, sisters, nuns), as well as many lay Catholics, several times every single day, as they observe "The Liturgy of the Hours".
Jesus (who is referred to many times in the New Testament as the "Son of David") and His first Apostles were all Jews, and the first Christians were all Jews who had a background in Judaism. (And Jesus also quoted a Psalm attributred to David from His Cross.)
I urge you to do the following searches on Google (without the quotes):
"is david's tomb the real one"
"prophetic references to Jesus in the Old Testament"
"books on prophetic references to Jesus in the Old Testament"
I also highly recommend you read some of these books and articles: