It was always my understanding that Israel will accept the anti-Christ as their leader and as the messiah. If that truly is the fact, then would they not follow his genealogy back to David?? Wouldn’t he have to be a Jew?
It’s important to remember that only believing Jews will reject the anti-Christ, and they won’t do this until he claims to be God, at the beginning of the Great Tribulation. Prior to that time, the anti-Christ will appear to fulfill all of Israel’s desires. Chief among these will be giving them the go-ahead for their Temple. And in their history, another foreign king, Cyrus of Persia, was called a messiah (anointed one) by God in Isaiah 45:1. He also helped the Jews rebuild their Temple. So there is precedent for a non-Jewish King to be thought of as a messiah.
Also in Ezekiel 44:7-8 there’s a prophecy that upon His return, the Lord will accuse Israel of putting foreigners, uncircumcised in heart or flesh, in charge of His sanctuary during the Great Tribulation. I see this as a reference to the anti-Christ and the false prophet. Therefore I don’t think it will be necessary for the anti-Christ to be Jewish