>>Are there conservative Methodist denominations?
There are plenty of conservative Methodists and there are even conservative Methodist congregations, but the heirarchy of the church won’t ordain a conservative anymore, so as the old conservative pastors retire and die, we move more and more to the left. Quite a few non-denominational churches are very Wesleyan because they broke off from the UMC.
We don’t have many Free Methodist churches in the south. I think those are mostly a midwest thing. But, they are very conservative.
I believe the Church of the Nazarene is a conservative denomination that is based upon the teachings of classical Methodism.
Plus, there are many conservative Protestant denominations you can find a refuge in if you have to:
The Presbyterian Church in America/PCA(my denomination),
The Lutheran Church-Missouri Synod/LCMS,
Southern Baptist Convention/SBC and many independent Bible churches. Personally speaking as a conservative Presbyterian, I feel far closer to Biblically orthodox Lutherans, Methodists, Baptists, Bible Church folks, Nazarenes, etc. than I do to liberal Presbyterians.