Why are the reference alleles different from what I see in the literature, for example, A for T or C for G for MTHFR C677T?

Alleles are listed in the DNA plus orientation, AKA positive strand orientation as reported by the Illumina array utilized. The positive DNA strand orientation is by convention read from 5' → 3' direction. The minus or negative orientations is 3' → 5' and represents the complementary DNA strand. Since there is no standardized orientation commonly employed in the literature, some mutations are better known as reported in the minus direction. MTHFR 677TT is actually a negative strand name, and normalized to plus is actually 677AA. See the Orientation/Ambigous Flip FAQ for more information.