Well if you count decades old recognition of a state as a support of what is going currently in Gaza, i will not spend time to find any examples because on that premise you would be factually correct, but your premise is wrong. Past recognition of a state does not automatically mean support for its actions, which you seem to imply.
Coopertation on anything else with NATO not really adressing the point, as we are discussing the situation in Gaza specifically, not Israels ties with NATO in general.
Redditors?
About diplomacy 101 My country has diplomatic relations with russia for example. We do however not cooperate in most aspects. In fact we are on the list of their enemies.
My country also has diplomatic ties with israel. And we do cooperate. Mostly in education. My country is also a NATO member without a single US soldier or base present. Also opposed to current Gaza events.
Vermin psycho state is a bit too much for me. I'd just stop the discussion here.