My review of this episode is slightly hampered by the fact I haven't seen 'Hooves and Harlots', in which Gabrielle is apparently 'inducted' as an Amazon, but I maintain episodic television shows ought to be comprehensible no matter where you start! I feel the same way about book series, much to several friends' frustration.
The episode takes places in a healing temple (which looks distinctly Eastern of some description to me - whatever it is, it sure as heck ain't Greek!), in the middle of a civil war, and most of it revolves around arguments between Xena, who's practicing her battlefield medicine and teaching it to a young healer called Hippocrates, and Galen, the old physician who insists only Asclepius, the (correctly identified) god of healing, can decide who lives or dies.
The war was caused, according to the other side's leader, by the Thessalians (from an actual part of Greece) trying to force the 'Mitoans' (not from an actual part of Greece) to adopt their religion. This is spectacularly unlikely in an ancient context. The only religion that demanded that everybody worship their god and no other was Christianity, and they didn't start the more violent kind of evangelism until the medieval period. The only religion persecuted to that extent by polytheistic ancient pagans was, again, Christianity (because the Christians refused to worship the major gods, and therefore might endanger others) but the pagans were quite happy for Christians to worship their god, as long as they worshipped Jupiter etc. as well. Occasionally an emperor might take against a particular cult - the cult of Isis suffered this way once or twice - but always because of a specific grudge against that specific cult, not because they were against other religions in general.
Galen and Hippocrates are both named after famous ancient physicians, though Hippocrates is the better known - he is clearly the Hippocrates, he of the oath (we see him starting to write his famous works, all attributed here to Xena, at the end), whereas Galen is more of a fictional character designed to demonstrate how much superior Xena's practical healing is to his religious ritual. The real Galen was a Greco-Roman physician who lived in the second century AD and whose writing on medicine was still being used as a practical guide throughout the medieval period and even beyond.
Healing temples are something I happen to know rather a lot about, but instead of typing out a lecture, I'll just link to my paper on the subject, which is currently available here. As far as the argument between Xena's practical healing and Galen's more overtly religious methods goes, I personally suspect that all these places practiced practical healing as well as religious rituals, but proving it either way is pretty much impossible. Civil war aside, chances are these temples were usually filled with people whose problems couldn't be cured by local healers or practical healers anyway, and pilgrimage to the temple was their last resort - I suspect there were healers there who did their best, but there was often little they could do anyway.
If you were going to have a baby, on the other hand, as Gabrielle's friend Ephiny is, you wouldn't want to go anywhere near a male healer of any kind, they wouldn't have a clue. You'd need a midwife, and they would definitely favour practical healing, though I'm sure they'd have some religious rituals as well.
Ephiny is apparently an Amazon, who was on her way to Athens because her recently deceased other half wanted their baby born there. At first, she doesn't specify why - better medical care? You'd want Cos or even Epidauros for that. Citizenship? You can't get that from geographical proximity, you have to have two Athenian parents. In the end, it turns out the Athenians are 'more tolerant' - presumably of mixed race marriages between centaurs and women. There's no historical evidence for that, oddly enough!
The other main storyline of the episode follows the Mitoan leader who is eventually persuaded that war is, generally speaking, not a good idea. It takes a story, a baby centaur, lots of preaching and several deaths (including, briefly, Gabrielle's) to convince him, but he gets there. I love that Gabrielle self-identifies as a bard. The nice little story she tells about finding peace in yourself is not, you'll be unsurprised to hear, an actual Greek myth, though Artemis turning people into hunted animals features in actual myths.
Not a bad episode, but a woman giving birth to a centaur? Really??!! At least when Doctor Who featured human/kitten hybrids, we didn't have to actually see the birth. And if Xena did an ancient Caesarian section that left the mother alive, she really does have magic powers. We do get another great disclaimer though: Being that war is hell, lots of people were harmed during the production of this motion picture (but since television is a dramatic medium of make believe, all casualties removed their prosthetic make-up and went home unscathed).