I think we need to submit the word “frum” for inclusion into standard English dictionaries. There is no other practical standard English alternative.
Calling myself a “religious Jew” puts my practice standards on the same level of perception as the barely practicing: the folk who may wear pants, pat coworkers on the back, and don’t make a big fuss about things like being asked to go for a coffee run at a non-kosher restaurant.
“Orthodox Jew,” is often misunderstood, though. Unless someone has had considerable contact with frum Jews in the past, calling myself an Orthodox Jew not ring any bells in terms of practice and possible accommodation I may need. It’s also unwieldy, being two words and not complying with easy grammatical conversion (Orthodox Jews or Jewish People do not do “x” sounds either lumpy or truncated, and unnecessarily accusatory or overly PC).
I’ve noticed a tendency to shorten one’s description to simply “Orthodox.” This is not a good idea. Why? I fell into this habit for a little while as well, until I was permanently cured of it in the course of a single conversation. I described myself as Orthodox to a non-Jewish underclassman, to be told “Me too, I’m also Orthodox! Coptic Orthodox!”