If Palestine got to have its own recognized (by everyone including Israel) and sovereign state, what other different current nation would it most likely resemble?

what that would mean for women, gays, children, people of non-muslim religions, in terms of personal freedoms, etc

So the wonderful thing about anti-colonial movements is that even if they start right wing they have to get more left wing as time progresses, simply due to the power dynamics that are created through the process of throwing out the imperialists. Once you stop foreign oppression, you have a grassroots mass of militant and armed revolutionaries that you're accountable to and who get upset when you try to reproduce the same economic system. You also are tied at the hip to them as the imperialists seek a return to an old system.

This includes movements where there is no significant communist presence, but it happens faster when there are communists.

Luckily, the PLFP is the second biggest party represented in the Palestinian joint operations room and have significant military and political power, meaning that in Palestine it probably will take a lot less time to materialize.