They have multiple.

There is the obvious split, Israeli and Palestinian.

Then, there are the Druze awkwardly shoved in the middle as the "acceptable" racial minority that they leverage against the Palestinians.

There is deep white supremacist strains, where black Jewish people are treated as lesser, including even sterilization.

One of the biggest internal splits, and the one perhaps most dangerous to the State, is the Haredi groups, which are a flavor of ultra-orthodox Judaism. They have an exemption from serving in the IDF, which they very much take, "studying the Torah" instead. They are the main driver of population growth in Israel, generally aren't super wealthy, and are opposed to serving in the military, albeit for selfish reasons rather than moral. Collectively, this is a very big issue for the Israeli project that's silently growing in the background. They're also incredibly regressive in regards to stuff like women, which isn't a surprise.

They aren't the only strain of reactionary though of course. There are soooo many different fucked up groups in Israel trying to enact their great future vision. There's a reason why Netanyahu is "the Moderate" by those who get Israeli society. It gets so much more insane. Some of these groups are more secular, many are religious, but all of them are tearing into the base foundation of the society. They are also all conditioned to commit horrific violence by the nature of the Israeli state.

This is all of course surrounded by an increasingly strained and isolated Israeli economy leading to worsened living conditions, worse employment and so on. It's an incredibly unstable powder keg. It's only a matter of time until the knives start turning inward, in a very bloody way.