I suppose technically the best term to use is already being used by the religions in question. A person who followed the teachings of Jesus while thinking he just had pretty good ideas but wasn’t holy would be a Christian in the same way people are Freudians and so on. I would use those words, except they’d cause confusion. I suppose the best term might be “atheist Christian” “atheist Buddhist” and so on, though likely you’d have to answer questions there, too.
And there was me thinknig there was a simple, obvious, term. ISTM that ‘culturally X’ is the best fit.