Sure. One among many. They’re influential, but not deterministic.
> that they've paid $53M to politicians
No, they don’t. They’re reporting campaign donations.
There is a tendency, when we disagree with an election, to tally up the donations made to the other side while ignoring all the times the best-funded candidate got trounced. (Jeb!) The influence of money in politics is one of sharply-diminishing returns. It is invaluable for name recognition. It doesn’t swing people on fundamental issues.
Israel has had unique sway in America because for most of its history it has been uniquely popular. Partly because of our Jewish diaspora. Partly because they were a reliable ally. And partly because they give us a lot of money. But two out of three of those factors also apply to the Gulf states, and we tend to be a bit less deferential to them because they’re just not as popular.