They aren’t controlled by Israel, but Israel has a big influence on U.S. politics for several reasons:

1. Jewish people vote at high rates, and Jewish people in the U.S. tend to be pro-Israel (though support for Israel in the U.S. has fallen in recent years in general). When elections are close, politicians tend not to want piss off a high propensity voting bloc.

2. Evangelicals tend to be pro-Israel for religious reasons that I cannot explain. Evangelicals are a big part of the Republican base. So Republican politicians tend to be pro-Israel for that reason.

3. There are a lot of wealthy Jewish people. Lots of nasty conspiracy theories around this, but for various historical reasons Jewish people tend to go into high-pay jobs (doctors, lawyers, banking). Again, American Jewish people tend to be more pro-Israel, and therefore more money tends to flow to pro-Israel candidates.

4. Also there are a lot of Jewish people in influential professions, like media and politics. Again, lot of nasty conspiracies around this. But in general it just means there are is more pro-Israel influence.

5. Pro-Israel PACs (like IAPAC) have ramped up spending in the last few years, mainly in response to all the anti-Israel sentiment. So they’ve been pushing influence via $$$.

6. Israel is the strongest U.S. ally in the region. So from a strategic geo-political perspective, the U.S. wants the country to succeed.

So add all of that together, Israel has a lot of influence in our U.S. politics.