Palestinians are decedents of ancient Hebrews who were not exiled because they lived In rural areas and of Arabs according to Israeli scientist tvsi Minai. Some Jews aren't really jewish but are just Russian or Polish but don't know that. That's why some have blond hair and blue eyes-not common for someone with full middle eastern ancestry. For Muslims, Christians and Jews Jerusalem is holy so it belongs to all of them.
Palestinians being the Arabs who lived in the area defined by the borders of Palestine mandate have lived and ruled Jerusalem for as much as Jews have lived and ruled Jerusalem before the Roman destruction. Arabs took control of the city from 637 to 1967 with the exception of 120 years during crusades.
Without even making biblical references, the land should go to the Jewish people as the primary users. Some claim that since they were forced out and others moved in, that the immigrants now have a stake in the territory. Well, not all moved out. Some did accept a forced conversion to Islam and other just hid in secrecy. There has always been a Jewish presence. It has never been abandoned. Early settlers other than the Hebrews were primarily of European descent. Descendants of the early people that converted to Islam might have some stake in the area, However, the vast majority in recent history have migrated from Arab nations. They therefore have their own ancestral homeland if push comes to shove. The Jewish people only have Israel. Early conflicts circa 1900 were not primarily between Jews and Arabs. They were with Britain which was the occupying force at the time. The Arabian and Jewish descent seem to have primarily got along during that time. When the land was set aside to be Israel in 1948, it was not the Arabs they shared the land with that they had the conflict with. It was the blind archaic blind hatred of the neighboring uncivilized nations. The Jews at the time did not ask or force the Arab descent inhabitants out. The neighboring countries asked them to leave to be out of the line of fire, so to speak. The main source of turmoil in the middle East right now is due to the underdeveloped thinking of some Islamic people that want to use the Koran and their prophet as an excuse for their barbaric behavior. Genetically Hebrew and some Palestinians are close. There is no reason that these people shouldn't both inhabit the same land. The only prevention of this is the wild radicals that have made it into the political arenas in recent history that have been blinded to only state that the want the destruction of any and all Jewish.
No, Israel and Palestine do not have equally valid claims to Jerusalem, because the land was given to Israel. Although it may be hard for Palestinians to accept, they should learn to live peacefully in the land under the name of Israel. The Israelis do not want to destroy the Palestinians. Instead, the Israelis only want peace in the land that is rightfully theirs.