Both from the fun book What If #2:
1. Jerusalem, 33 CE - ignoring a hostile crowd screaming for blood, Pontius Pilate pardons Jesus Christ. Jesus returns home, under the protection of Roman soldiers.
The Romans decide they LIKE this kind of religious leader - he tells people to forgive their enemies and even to pay their taxes! What a guy!
Even though he is still around and presumably the Subject Matter Expert, Jesus lives long enough to see the religion he founded degenerate into innumerable squabbling sects. All claiming to be the Real Xians, of course. Jesus dies at the age of 90, blind and senile.
By then the Roman Emperor takes his title of Pontiff Maximus seriously. He becomes the Emperor-Pope, leader of the One True Xian Church, and ruthlessly cracks down on any hint of heresy or schism.
The Roman Army marches with a convert-or-kill mentality, always accompanied by a sub-army of aggressive Xian missionaries.
On the Roman borders the upstart sect of Islam pops up and is quickly exterminated, becoming a footnote in history.
By the 15th century, word spreads of new lands, across the oceans far to the west. They too will soon become part of the Holy Roman Empire...the REAL one.
2. Actium, 31 BCE - the naval forces of Cleopatra and Marc Antony defeat Octavian. Alexandria, Egypt, becomes the political, educational and religious center of the world.
Earlier members of the Ptolemy family were religiously very...flexible. Ptolemy I let himself be named "Pharoah," even though he was about as Egyptian as Liz Taylor and probably laughed at the whole idea in private.
The Ptolemies invented their own god, Serapis, and saw it spread far beyond Egypt. By the mid-First Century CE, Egypt is ruled by Caesarion - the son of Cleopatra and Julius Caesar. Who, following Ptolemaic practice, married his half-sister Selene - the daughter of Cleopatra and Marc Antony. IOW, one damn formidable family.
They hear of some useful new religious ideas percolating just over the Sinai border, in Palestine. So useful that they convert, as do all their citizens (except for Alexandria's thriving Jewish community, which all rulers had the good sense to leave in peace).
And the world sees the formation of...The First Church of Jesus Christ - Alexandria.