Why is a new coat of polyurethane tacky?
I had this issue with old trim that had a water based stain and a think coating of either poly or lacquer. You should take the door off and place it on two saw horses. I would start with a clean rag and lacquer thinner and try to wipe the door down. You should be able to get most of the finish off without doing a lot of harm to the stain. Once the poly comes off you will have a dull matte finish. If you apply "wipe on poly" after that dries you should get the sheen back. make sure you aren't scrubbing in one spot because you can over do some areas and kind of sand out spot from the wood. I also tried stripped but you need a lot of ventilation and a lot of rags. It was easier just taking the time and cleaning with the Lacquer thinner. They sell it at Home Depot for like $7.00. Acetone might work as well.