Yes of course Israel has a right to exist.
The case for a homeland for the Jewish diaspora was already strong before the Holocaust. Opposition to Israel by Islamic nations was met by astonishing success by Israel in 1948 and '67.
Israel's reaction to ongoing threats from its neighbours has at times been excessive and cruel resulting in terrible suffering that results in more hatred, more attacks and even more harsh reactions and so on....
Here is an interesting thought experiment though. If Hamas and Hezbollah unilaterally ceased all hostilities and put all its weapons beyond use tomorrow there would be peace and increasing prosperity all round. If Israel did the same it would be wiped off the map and once again become a victim of genocide.