In The Mandalorian they make a big deal of Mando never removing his helmet in front of others, yet characters like Sabine do it casually all of the time. Is this a contradiction, unexplained, or is there an explanation?
There's a couple of things at play here
Mandalorian has two meanings
In a normal world, Mandalorian would refer to people from Mandalore. In the Star Wars universe, everything is fluid. As such, a Mandalorian can also refer to someone who believes in The Mandalorian Way (I'll just call it The Way for simplicity, since that's all they ever call it in the series).
In the series, we learn that
Din Djarin (the namesake Mandalorian for the series) is not from Mandalore. He was saved by Mandalorians and became a follower of The Way.
Lots of retcons
There's no way to get around the fact that Disney keeps retconning Mandalorian canon. Current canon is
Mandalorians were a proud warrior culture that waged war against the Jedi (and presumably the Republic). Since [The Empire] dictates terms [after winning the war], Mandalorians were probably forced to disarm and shun lots of their traditional beliefs and customs.
As such, the best explanation here is that Mandalore Mandalorians weren't strict followers of The Way. After the Empire nearly wiped them out, The Way became a religion that anyone could become a follower of. As such, helmet removal became prohibited among its followers. The Mandalorian Episode 1 dialog supports this
KUIIL: You need to drop your rifle.
MANDALORIAN: I'm a Mandalorian. Weapons are part of my religion.