EDIT: I’m interested in how a free Palestine would play out in terms of what that would mean for women, gays, children, people of non-muslim religions, in terms of personal freedoms, etc.

The basis of this question is Zionist because it implies things would get worse for gay Palestinians, Palestinian women, and non-Muslim Palestinians. All of these populations are currently either under military occupation or in exile, banned from entering any of historic Palestine. They may experience oppression or marginalisation based on these identities, but all of them additionally are under Zionism's boot as Palestinians. When they are no longer oppressed for being Palestinian, it will be much easier for them to seek liberation along the other lines they are oppressed, such as gender, sexuality, and religion.

As for religion, some Palestinian parties are specifically Islamic, some are explicitly secular. It would be hard to say, but right now we are seeing very strong unity between the different Palestinian factions, including e.g. explicitly Islamic factions strongly condemning the attacks on Palestinian churches. Hamas, an Islamic party, is in alliance with the PFLP, which was founded by a Palestinian Christian and is explicitly secular. From what I can see, religion doesn't seem to be a hugely dividing line among the Palestinian factions, and I hope that will continue to be the case when Palestinians begin the process of recovering from Zionism and establishing a long-term state.

In any case, Hamas, one of the most influential explicitly Islamic Palestinian factions, is also explicitly supportive of religious tolerance in its charter, and envisions a Palestinian state in which people are free to practise their own religions. I am hopeful that the current religious unity we can see will continue after the fall of Israel.