The Reference Editor ID for the doors of player owned houses are not set to anything by default, but I need to set it so I can reference them in a script. Would this cause a conflict with other house mods? Or would it be only if that mod also changed the door reference editor id?

In effect you're replacing the door with one of your own, so there will be a few other effects.

Someone who installs your mod will be locked out if they didn't keep the key in their inventory. Your new door starts off locked, like the original, and becomes unlocked when the key is used. Unlocking the original copy of the door does not affect yours, so they have to do it again. No problem if they still have the key, but if it was left inside the house...

And that applies even if there's no other mod affecting the house.

If I was to change the ID of the door then discover is had conflicts and then change the ID back to empty like it was before. Will it still conflict even though I changed it back, or does the fact that it has been changed in the past cause a conflict?