The "doors" are limbs of a massive interdimensional eldritch being. A magic-user can bind them to our reality and coalesce their power into some sort of token, and those tokens can then be used to banish it back. For bonus points, this being could have some relevance to the game's overall plot (or it could be a Giant Space Flea From Nowhere bonus boss).

#Requirements:

Any "door" can be opened with any "key"

The tokens are interchangeable; they all contain the same magic.

Once opened the "door" stays open

Unless someone binds it again, at least.

It must be possible to purposefully construct a "door".

With magic.

The "key" can only be used once.

Using a token discharges its magic and destroys it.

Creating a "door" may require the use of magic but opening a "door" with a "key" should not require magic abilities

Anyone can use the tokens to banish it, all it requires is physical contact.

"Doors" are not portals. You can not teleport to a different location by walking through a "door".

Banishing it just removes an obstacle, you're left with an ordinary opening.

#Desired but not required:

The "doors" can appear randomly (like vines growing over a normal door)

Perhaps it can occasionally manifest itself into our reality without assistance? Though that would still require explaining where the tokens come from. Maybe the token manifests nearby in the form of a shiny object, which some critter takes away and hides.

the "keys" should be rare but it should not be obvious where to find one (for example if only rich people could possess them, it would make no sense to search for a key in a poor man's house)

Tokens would be wherever the magic-users decide to put them, so that isn't a problem unless they all have consistent habits (or see above).

The "doors" are limbs of a massive interdimensional eldritch being. A magic-user can bind them to our reality and coalesce their power into some sort of token, and those tokens can then be used to banish it back. For bonus points, this being could have some relevance to the game's overall plot (or it could be a Giant Space Flea From Nowhere bonus boss).

Requirements:

Any "door" can be opened with any "key"

The tokens are interchangeable; they all contain the same magic.

Once opened the "door" stays open

Unless someone binds it again, at least.

It must be possible to purposefully construct a "door".

With magic.

The "key" can only be used once.

Using a token discharges its magic and destroys it.

Creating a "door" may require the use of magic but opening a "door" with a "key" should not require magic abilities

Anyone can use the tokens to banish it, all it requires is physical contact.

"Doors" are not portals. You can not teleport to a different location by walking through a "door".

Banishing it just removes an obstacle, you're left with an ordinary opening.

Desired but not required:

The "doors" can appear randomly (like vines growing over a normal door)

Perhaps it can occasionally manifest itself into our reality without assistance? Though that would still require explaining where the tokens come from. Maybe the token manifests nearby in the form of a shiny object, which some critter takes away and hides.

the "keys" should be rare but it should not be obvious where to find one (for example if only rich people could possess them, it would make no sense to search for a key in a poor man's house)

Tokens would be wherever the magic-users decide to put them, so that isn't a problem unless they all have consistent habits (or see above).