For instance, my family (no members of which are theatre-savvy) easily know about Phantom, Cats, and Jesus Christ Superstar. They can even sing a line or two of a song from those shows. If I asked them to name a song from Carousel or Oklahoma, they'd be stumped.
Unless that has more to do with the fact that Rodgers shows are significantly older.
It could be that or the age of the person you are asking and/or their preferences. Ask them about a song from Sound of Music and I'm sure they'll come up with more than one. King & I and South Pacific have major classic hits as well. All three of those have songs that are probably more commonly known by the general public today (Sound of Music, Do Re Mi, My Favorite Things, So Long Farewell, Edelweiss, Climb Every Mountain, Shall We Dance, Getting to Know You, Wash That Man, Some Enchanted Evening) than Carousel or Oklahoma.
"What can you expect from a bunch of seitan worshippers?" - Reginald Tresilian