Our 80's pop station here goes full Christmas music between Thanksgiving and Christmas, and they play Mary Did You Know.
I've heard it show up in the background of some film scenes, can't remember if it was a movie(ies) or TV show(s) or what...I just know I've heard it here and there.
I don't recall ever hearing it on any secular stations in Austin at Christmas time, though, and I agree it's lesser known than Mariah Carey's tune. I guess I hear it enough (even a few "secular" artists have covered it) that it passes for me. Then again, I'm more likely to hear something that appears mainly in a religious context than some others.
I did think Wham's Last Christmas should qualify. Maybe the Band-Aid song as well. Radio stations do play them, though not as much as the other old standards.
The Jackson 5 have some Christmas songs, I'm assuming from the 70's, that get a ton of play and most people recognize them. Notably 'I Saw Mommy Kissing Santa Clause' and 'Santa Clause Is Coming To Town.'