So, I haven't fully re-read the series in over a decade.
From what I remember, any religion was in-universe-accurate. It approches things from a historical standpoint, not religious. And in the time period those myths are set in, the people in Britain were in general converting from pagan cultures to ones with christian influence. The characters themselves practice a mix of pagan influence and christian ones.
Like, the Britain in the series is one affected by the history of Roman colonization in the south, with more pagan influences the further from London you go. So characters that were a part of the roman legions are going to be more christianized, and ones that weren't aren't necessarily.
Let's say you picked up a semi-historical fantasy set in Japan. Historically, it's accurate that any given character in such a book would practice one of the religions common in Japan in that period. It's would be atypical in some regions in some eras for someone NOT to have some level of identification with the local religion.
This series is like that. Yes, the influences of religion on the characters are present. Is it a thin-veiled attempt at preaching? No, not from what I recall. It's possible modern discourse might have changed my viewpoint, as I mainly read this series pre-internet (late 90s, early 2000s), but I did not find religion in this series overbearing last I read it.
I don't remember many details from the series, but I remember vividly that one character, I THINK Merlin's mother, was a pagan priestess bullrunner in her youth? From Atlantis? And I don't remember her becoming a zealot christian or something. It's possible she might have converted later in the books and I don't recall as the culture of Atlantis gets diluted due to it being destroyed, but if she did it would have been in a more historical manner.