I find this whole thread a bit confusing—the comment two up describes “orthodox” meaning one-true-way as a Russian thing, but this is also part of the connotation in English.

You describe it as not having this “one true way” connotation, but as having this pointlessly rigid connotation. In English, I think it has both connotations. Although, almost any phrase which has an implication of “one true way” can end up with a double meaning of “pointlessly rigid,” right? (It is context dependent, of course).

православный is used in jargon for exactly that meaning. source: 45 years of native Russian speaking.