Did you leave the closet before the unlock paper showed up? Fairly certain it doesn't give the unlock if you leave before that... or at least that's how it used to be, idk if that got patched.

Still works like that. You have to wait

Did you touch the character in the closet and then immediately left? If you don't wait for a few seconds, it can mess up the unlock.

Oh, I didn't know that :(

Skill issue 

Did You get turned into another character? (Lazarus rags, ankh, clicker?)

No

Have you touched the entity in that Red Room?

Yes

Skill issue 

Did you open the red door in Home?

Yes

Were you playing local co-op? If so, you always unlock player one’s character, regardless of who uses the key.

No

Was it with a seeded run/victory lap/rerun?

No

Mod issue