> How likely is it that those "protestors" are US and Israel propped

It's almost sure that both US and Israel are meddling with the current situation. That doesn't mean the situation isn't also started by and wanted by the population.

For a comparison point in the past, the civil rights and antiwar movements in the US were grass-roots movements started by local people with legitimate claims. At the same time, opponents of the US like USSR were involved in stirring these movements, because of course they would.

There isn't much you can infer about the legitimacy of a movement by learning that the movement is helped by foreign intelligence agencies.

The best way you can avoid this kind of confusion is 1) make a society in which malicious actors don't have many latent issues to stir, and 2) make it so your country's intelligence agencies aren't malicious actors. There isn't much else to do.