You blame 1967, but actually the year 1974 is very significant. It was after the Yom Kippur War of 1973 (
https://en.m.wikipedia.org/wiki/Yom_Kippur_War). A surprise attack launched by Syria and Egypt on the holiest day of the year when all Jews are fasting. Isreal was able to fend them off and that's when Arab nations started to focus on PR campaigns and UN (and FIFA) resolutions as a way to destroy Israel.
Also very interesting to note: the Israeli Football was called the Palestinian football association from 1929-1948, even though it was made up of Jewish, Arab and British (stationed soldiers) players. "Football has a long tradition in
Israel. The game was originally introduced during the time of the
Ottoman Empire. The Palestinian Football Association was formed in August 1928, and joined
FIFA in June 1929, but at the time the association was made up of Arab clubs, Jewish clubs, and clubs representing British policemen and soldiers serving in the region during the British Mandate rule that spanned the period between World War One and the creation of the State of Israel in 1948. The British Mandate of Palestine national team made its debut against
Egyptin
1934 FIFA World Cup qualification, losing 1–7 in
Cairo. The team played five international matches, including a friendly match against
Lebanon, until the British Mandate for Palestine was dissolved.".
https://en.m.wikipedia.org/wiki/Israel_national_football_team
I won't take the last part any further, because it could go way off scope. But I will end by saying that all Israeli citizen arabs (Christian, Druze, and Muslim), as well as LBGT all have the same rights in Israel as any other citizen. This includes playing for the Israeli national team. Case in point Bibras Natcho (
https://en.m.wikipedia.org/wiki/Bibras_Natkho). Unfortunately, the same freedoms cannot be found in any neighboring Arab nation.