Yes indeed.
When I went to Israel in 1984, I was able to Visit The Cave of Machpelah (Abraham’s Tomb) in Hebron, The Church of the Nativity, the Shepherd’s Fields, and Rachel’s Tomb in Bethlehem, Mary’s Well in Nazereth, The Tel in Jericho, Joseph’s Tomb in Shechem (Nablus), Lazarus’s “house” in Bethany, and of Course, the Temple Mount.
Perhaps the Bethlehem sites are still accessible, due to Christmas Tourism, But Joseph’s Tomb no longer exists, and the Temple Mount is off-limits to Jews and Christians.
When Israelis control the sites, they are open to ALL.