I would guess that the doors are original but I don’t know for sure. It must be the climate that has kept most of the wood doors in SMA in such great shape. I haven’t found much history on the building, but here’s a little:

This mansion was built between the late 18th and the early 19th century, and gracefully unites three architectural genres: baroque, rococo and neo-classical. During the War of Independence, the Casa del Mayorazgo de la Canal was pillaged by Spanish forces and the mansion’s proprietor, Narciso María Loreto de la Canal, was captured and thrown into prison, where he died in 1813. Upon the victory of the independence movement, however, the house was returned to the Canal family. In the late 19th century, the building was converted into a hotel, Hotel Allende, and by the 20th century, it was acquired by Albino García. In 1981, the property was bought by the National Bank of Mexico, and in 2010, during the celebrations of the 1810 War of Independence, the National Bank converted the Casa del Mayorazgo de la Canal into the Casa de Cultura Banamex, by agency of the prestigious cultural foundation Fomento Cultural Banamex. Today, people can visit the mansion to see temporary exhibits, the video room, the bookstore and the folk-art gift shop. This building is, unquestionably, one of the finest examples of New Spanish civil architecture in the region.