I, uh, am not sure how a person can hold those views simultaneously.
Success of Palestine will mean oppression of the groups the cause seeks to protect (LGBTQ+ specifically).
Isn't this "paradox of tolerance"-esque, or is there a belief that if the Palestinian people were not being bombarded by an oppressive force: that they would be equitable to LGBTQ causes.
Or: does it not factor into it at all?
For example, right now the USA is quite progressive in general with gay rights compared to many places, which is great, but I would not support the US government invading other countries, or going back to colonization etc.
I can see those two might be opposed if what you wanted was LBGTQ rights at any cost. But for me at least war, and especially one-sided war, is the bigger injustice and other issues are secondary to that.
That depends on what you mean by success of Palestine. Eg if all you're talking about is an end to the current war, that's not really true.
In a lot of ways, the struggles are similar to BLM - there is a great injustice being done by a powerful force funded by the US government. Or again with opposing the US's global war on terror. The people in those groups aren't forced to be on the palenstinians side, but it is logically consistent with the other two.