None of these wood species are inherently weather resistant. They all depend on the paint, stain or sealer finish for weather protection. So the answer to your question is found in how you propose to finish the door.

Maple is a light and very hard wood, It will take stain, sealer or paint equally well. Douglas Fir is considered a soft wood, but one with great structural ratings, when used in framing lumber. It is a light wood, but not one that is particularly attractive when stained, IMO. Mahogany is a dark wood, and probably the most naturally weather resistant of the three. It becomes even darker when stained or finished with a clear sealant. Painting Mahogany makes little sense.

Hope this helps. Good luck with your project.

So much depends on whether you will paint or stain the door, or you think you will leave it weather naturally. The latter is probably a mistake.

Most commercially available doors today are veneered so the species will not matter much of it is veneered.But if your going to go with a custom solid wood door I would choose Mahogany, just make certain they use Genuine Mahogany (Swietenia macrophylla) and not one of the types of wood that is sold as Mahogany today.

Are you building frank betz candler park. I thought I saw some pics from u. Do u have front, rear and interior pictures? We are going to build this house but I would like to have your thoughts on the plan and any modifications you came up with.