Methodists probably lean Republican, although the official church itself (not necessarily individual churches affiliated with them) is fairly liberal, although I may be completely wrong. I attend a Methodist Church, but I don't really fit in with any single denomination.
A lot of Churches use the name "Methodist"
without being what is normally termed Methodists...
I'd guess that "orthodox" Methodists (ie: United Methodists) are Dem leaning... but certain other groups are
de facto fundamentalists...