The two will be joined together in the future:
"And the woman was arrayed in purple and scarlet colour, and decked with gold and precious stones and pearls, having a golden cup in her hand full of abominations and filthiness of her fornication: 5. And upon her forehead was a name written, MYSTERY, BABYLON THE GREAT, THE MOTHER OF HARLOTS AND ABOMINATIONS OF THE EARTH. 6. And I saw the woman drunken with the blood of the saints, and with the blood of the martyrs of Jesus: and when I saw her, I wondered with great admiration" (Rev.17:4-6).
Rev
18The woman you saw is the great city that rules over the kings of the earth.
Rev
8Their bodies will lie in the public square of the great city—which is figuratively called Sodom and Egypt—where also their Lord was crucified.
The Woman riding the beast (The Anti-Christ) is Jerusalem.
When the the Jews rebuild their third temple they will select a new High Priest to rule over it. At this point Israel will once again become a fully fledged Theocracy again, just as it used to be and so the high priest will rule over Jerusalem and Israel too. By this time Israel will also be the most powerful nation on Earth just as Jesus said:
Luke 21
29He told them this parable: “Look at the fig tree and all the trees. 30When they sprout leaves, you can see for yourselves and know that summer is near. 31Even so, when you see these things happening, you know that the kingdom of God is near.
The high priest will be saying the Jewish messiah is about to come (and being very Jewish he will also say that Jesus is most defiantly not the messiah) As such he will be falsely prophesying; A false prophet.
The most powerful man in the world, the Jewish high priest, falsely prophesying against Jesus.
He will be the false prophet of Revelation.
Over the 7 year tribulation he will be forced to work with the Muslim Mahdi Anti-Christ but they will hate each other:
Revelation 17:16
The beast and the ten horns you saw (The Anti-Christ) will hate the prostitute (The false prophet). They will bring her to ruin and leave her naked; they will eat her flesh and burn her with fire.
The tribulation begins in 2022.