In Dreyer/Schmitt, "bäckt" is given as the primary third-person form of "backen". Since I never used this and have not heard it often where I live (Northern Germany), I was very surprised by this and wondered if this could be right. Are both forms still equally valid? Are there regional differences?
Both forms are equally valid. The differences are regional in use, not in meaning. I did find that "backt" is sometimes listed as the more informal of the two, but that may again be regional. Both forms can be used equally, as opposed to something like "buk" (rather dated or extremely formal) vs "backte" (standard) for the past tense.