No way home: Fireball by John Christopher (Puffin, 1981)

Two boys, one British and one American, are swept up by a fireball and landed in the Roman Empire. Except it's 1981 and Christianity is a minority religion.

Christopher does a good job of explaining why the world hasn't changed much -- little incentive, stable worlds are actualy more common--and of detailing the boys' rivalry (they are cousins). He also makes it clear fairly early on that they aren't going back, which helps contextualise their decision to aid a Christian revolt.

Brad (the American) shows the Bishop stirrups and long bows. This is the one implausible bit because longbow wood has to be seasoned, and learning to use a long bow *fast* is not a short job (see Bowman of Crecy). Even making arrows is a skilled trade (frankly, a better choice might have been the crossbow, there's some argument that Crecy was a fluke).

The Christians win, even taking Rome. At which point the Bishop demands forced conversions using "the pendulum' (Straight out of Poe) to enforce it) Simon, Brad, a gladiator called Bos and a pagan caled Curtius (who refuses to convert) set sail for the new world. Simon goes only when he realises the girl he loves has long been betrothed to a man he loathes, and that he doesn't understand the social structure at all.