They always co-op black people's struggles but rarely will you see them address the anti-black racism within their communities.
Some things I observed from living there:
(1) As a whole, both groups are racist to black people.
(2) There's some good people in both groups (although I found the Palestinians to be more hospitable).
(3) Many Palestinians are very aware of how they're perceived by the outside world so I would take all of this support for BLM with a pinch of salt.
(4) Israel is very blatant with their mistreatment of the Palestinians. They don't even try to hide it. It's despicable.
(5) Most Israelis are MENA Jews who came to Israel from the late 1940s to early 1950s. Many were fleeing persecution in those countries, which came as a result of the creation of the State of Israel in 1948. I think this is an important note in understanding why there is so much hatred on both sides. The cycle of violence has been going on for over 100 years.