No, this isn't true. Jewish is an ethnicity that crosses multiple "race" backgrounds.
Say what now?
Of course, racial categories are made up anyway, but some people seem to care about these things.
Ironically, the Sephardic and North African Jews that I know are more likely to self-identify as nonwhite, but are probably still counted as white by the US Census. Goes to your point about made-up categories!
In politics, people are typically arguing for their positions, and thus you can't take simple statements of fact apart from what the speaker is trying to achieve. Basically: why is the speaker talking about Jewish people on power so much? Why do alt-right people love to talk about black crime statistics? Both of these things can be true, but they're not just making random statements, they're trying to imply their arguments. It's dogwhistling, basically.