I have some 4 panel pre-primed masonite textured doors for my basement. We're going for an Old World look with a bar that my husband is building out of red oak that will be stained a medium oak color, wine cellar and media room. With the cost of good quality real wood doors and trim that takes stain evenly, we opted to paint the trim and get masonite doors. Since the bar will be stained a medium oak I'd like to paint the doors to go with the stained bar. I don't want to go to the trouble of faux finishing the doors to look like wood grain. Maybe a glaze or something? Any ideas?

Once again a pro paint store can be your best option for specific advice on painting and staining to create a wood look finish and match other wood colors.
Sherwin Williams or Benjamin Moore are a couple that are common and have trained employees to answer your specific questions.

I would first get a sample of the finished stained woodwork, and have them help you get a match to create the same color on the doors.

I saw on line a product by Rustoleum called Cabinet Restoration. It's basically just painting the doors and rubbing a glaze on them with cheesecloth. I wonder if that would work on masonite doors?

Just was told by a Rustoleum rep that this product will not work on anything with a texture.