Unfortunately a lot of Americans apply a US-centric viewpoint on foreign nations and that's where a lot of confusion comes from. They understand Israel is a democracy but fail to understand that democracies aren't always cookie-cutter versions of their American interpretation. So, they form their opinions based on what little they've heard and what little they understand. What exacerbates the issue is when they come from echo chambers, where beliefs are amplified irregardless of whatever evidence exists for or against their stance. Misunderstanding the Israeli election process isn't a uniquely American phenomena - I've seen it from others worldwide - but as I'm American (with Israeli family, so better informed than most) I do see others talk about it and fail to truly get what's going on, especially from those who don't understand how Netanyahu keeps getting elected or what is the primary concern of the Israeli populace.
To be fair, you may not understand American society yourself. While a lot of Republicans and the specific Trumpsters do view Israel positively for anti-Muslim sentiment, I dare say their positive affinity for Israel is a bit more genuine as a whole. A lot of concern isn't off of bigotry for another, and is welcomed. There is concern for the Jews and it doesn't always have to be because of anything to do with extremist Islam. Furthermore, it's not like the opposing political sphere has a better understanding of Israeli politics, especially the far-left who doesn't bother to check their facts and just paints Israel as a demonic entity. I spend more time correcting those on the left when it comes to Israel, which doesn't bother me as a centrist but is noted nonetheless.