Nearly all containers (glass or plastic) need to have their label removed to recycle properly. And you must rinse them out, too.
Some can be recycled with the label on, but only if the plastic used is the type that can be recycled. Confusing and frustrating, yes.
The crappy thing is that some labels really don’t come off easily because they’ve been glued in place… those are awful to recycle because it requires quite a bit of extra effort, soaking, adhesive remover, etc… 😂