I am an advocate for a Bi-National One-State Solution, where Palestinians and Israelis have equal rights, including right of return. Where Historic Palestine can be a safe haven for all Jewish, Christian, and Islamic people from persecution. A Two-State Solution is no longer viable due to the land grabbing of Israel, that has divided the West Bank into hundreds of isolated enclaves surrounded by military checkpoints and violent settlers.
I do not think Hamas nor Fatah should govern the Palestinian people, both are corrupt for different reasons. However I don't think any meaningful change in governance can happen until an end to the Apartheid/Occupation, for the same reason of how Fatah and Hamas are corrupt. A free and fair election cannot happen under an Apartheid State.
Your fear is understandable, however I think it is misplaced. Anti-LGBT+ is shared between all conservative reactionary governments, regardless of religion. American conservatives are just as anti-LGBT+ as any middle eastern conservatives for the most part. Neither Muslims or Arabs are monolithic, there are still advocates for LGBT+ rights in middle eastern countries. In Palestine, for example, there is ASWAT and JOH. Israel is a little better for LGBT, however there has been some pinkwashing.
Right now, no Palestinians in the Occupied Territories have rights, neither basic human rights nor civil rights. I'm an advocate for all people to have those kinds of rights, regardless of whether they agree with all my views or not. So, even if the majority of Palestinians are anti-LGBT, I will still advocate for them to have those rights. I will also advocate for LGBT+ rights within Palestine.
I do have a Bachelor's in STEM, however I'm not a historian. A year ago I had no idea about the situation in Palestine/Israel, nor the history. The best resource I've found by far for extensive research on the history and on-the-ground investigations are New Historians and Human Rights Organizations respectively. Here's a list of the ones I recommend.
List of Books by New Historians:
If you don't have access to a library or want to view these for free first, they can all be found on the Library Genesis. I believe a few are on audible too