Why would it? We have lots of friends of X groups that don’t need to.
The strongest own goal Israel’s political opponents in America play against themselves is in pretending this is entirely a conspiracy. It’s not. Until recently, Israel was popular. Against the background of few voters caring about foreign policy at all, that meant small margins were foreign-policywise meaningful while continuing to be electorally irrelevant.
Yes, it's why we require foreign agents to register [1].
[1] https://en.wikipedia.org/wiki/Foreign_Agents_Registration_Ac...