The stain will be a wood preservative - to prevent rot.
The wood of the door will still get wet and expand and then contract as it dries. Over time the glued joints will be loosened and the door ruined - probably permanently.
Most exterior wooden doors are painted - some have exterior grade varnish to act as a weather barrier.
I suspect you will have to paint or varnish your door but you might try several generous applications of Teak Oil or Danish Oil - but not until it's been allowed to dry out.
Peccavi
January 2011