Either intentionally, or unintentionally you have totally distorted the meaning of the term. You can vote for whomever you choose. The folks who are termed Israel-Firsters are those who attempt to push US to act against its self interest for the benefit of Israel. If for instance you were in a position to push US into yet another war when it's clearly the last thing US needs, you would be an Israel-Firster. There are 3 million Greek-Americans. Are they fighting to have US bail them out? Nope. But if it were Israel that was at risk of bankruptcy, you can bet SOME American-Jews would do exactly that, and they would rightfully be called Firsters.
Alleged Jerusalem gay pride parade stabber's remand extended by 12 days (Haaretz)