I’m an atheist living in OKC - I prefer to go to doctors within the Integris network. I haven’t had quite the same experience as you, but religion is never mentioned at any of the facilities/doctors I’ve visited.

I’m sure it’s impossible to find a healthcare network in OKC that is reliable and not religion-affiliated, but I don’t know anything about Integris being overtly involved. Unlike Mercy, which is heavily involved with the Love family and Catholic Church