[Masterwork]

Do NOT just stain one side and then clear. If your clear wraps around the back by accident, your stain won't hit any bare wood. And if the stain hits the back, you'll have uneven spots, later. You should be fine to stain both sides at once, just leave the outside of the door facing up.

Any issues, re-wet the spots with more stain and rub them out with a rag.

 

[Masterwork]

Birch doesn't need sealer/conditioner, actually. I've stained and cleared countless birch veneer doors for schools/offices. Maple is pretty bad, though.