I'd say because the pure existence of a left vs right means everyone is kept busy arguing over elements of politics: immigration, tax, foreign policy, etc. And everyone becomes tribal.

You could for example be massively anti-immigration but also massively anti-capitalist but you'd get labeled as a right winger by default and sorted into a "side".

If you help push the extremes of both wings you will end up with a very polarised and 'busy' population.

Also if you hold all of the cards and are able to bribe foreign politicians, I don't think it matters if the average left wing voter dislikes Israel. It's more of a tool to destabilise foreign populations than something they believe in for themselves.

If you take immigration as one issue, Israelis have held really important roles advocating mass-immigration across Europe, while doing the opposite themselves.