Using Shrink Item on a locked door should work fine
A door is a discrete item, no matter if it's closed or open. Doors – even barred ones - are referred to as items/objects in the rules (for example, in the section on Breaking and Entering in the Player‘s Handbook (p 165)).
The description of the Shrink Item Spell doesn't say that the spell won't work if the target item is held or restrained by some other object, creature, force or magic (as long as the target isn't a magic item itself). So I see no reason to rule that a door can't be shrunk because it is locked or fixed in it's hinges.
The given example "Even a burning fire and its fuel can be shrunk by this spell" rather suggests that a DM should feel encouraged to be generous about what can be a valid target for this spell and what can be achieved with it.