At the moment, I'm only getting to play AL at cons, where I'll typically play 9-16 games depending on the con...
Anyway, I have NEVER played in a game with a Multiclass character in 5e.
It's actually really odd to me, since back in 3.X almost everyone MC'd often into 3 or 4 classes.
But, to me, MCing in 5e isn't something I've done because the baked in class archetypes allow for most of the things I would have MCd for in earlier editions.
Like, Eldritch Knight and Arcane Trickster. Or the different bonuses Cleric domains give them.
Also, taking away the differing BABs and iterative attacks of 3.X, the overall effect of MCing on a character seems much less to me.
EDIT: Additionally, It seems to me like in 3.X, MCing was generally done when you hit a swath of boring levels, like, oh all the next five levels of this will get me is more uses of this power, nothing actually new, so you MC into a different class instead to get NEW options. And in 5e, they've done a very good job of not having to many boring blocks. All the classes get something new and interesting pretty much every other level at least.