I can't speak for the protesters, of course, but I believe it is consistent with the goals of the BDS movement.

"Do you have any insight into whether the protesters there think Israel has a right to exist at all..."

Well, the claims that the protesters want to push all Jewish Israelis into the sea is a ridiculous lie, to start with. If your definition of "Israel" is "A Jewish state, explicitly designed along religious lines, giving Jewish religious leaders greater rights over public policy than people of other religions and non-religious people" then I would say the protesters oppose that vision of what Israel should be, preferring a democratic, multi-ethnic state with equal treatment for people of ALL religions.

The comparison I'd make is to Christian Nationalists, people in this country who believe "The United States is a Christian Nation" and that Christian leaders should therefore have outsized influence over public policy. Or Narendra Modi's vision of Hindu Nationalism.