> I agree with the sentiment, but unfortunately often this is too simplistic. For example, a lot of Palestinians are not tolerant towards LGPT people -> a lot of LGPT people are not tolerant towards Israelis -> a lot of Israelis are not tolerant towards Palestinians.

Nice bait with broad sweeping generalizations there.

One of critiques of "Paradox of Tolerance" is its proponents (probably not Karl Popper himself) take the argument to its extremes (similar to the generalization you posit), while the reality is more of a spectrum.