Since Gilead is a fundamentalist Christian regime, why would the Baptists rebel against it?

There are several reasons why Baptists would rebel against the regime in Gilead. For one, the leadership in Gilead seems to have adopted a more Old Testament mentality, and the Baptists are much more New Testament, Jesus-centered. Gileadeans have based their society on the story about Rachel's inability to bear children for her husband, a story from the book of Genesis, the first part of the Old Testament. Further, the term "Handmaid" is likewise introduced...

There are several reasons why Baptists would rebel against the regime in Gilead. For one, the leadership in Gilead seems to have adopted a more Old Testament mentality, and the Baptists are much more New Testament, Jesus-centered. Gileadeans have based their society on the story about Rachel's inability to bear children for her husband, a story from the book of Genesis, the first part of the Old Testament. Further, the term "Handmaid" is likewise introduced in the Old Testament. Baptists, on the other hand, place a great deal of importance on accepting the love of Jesus and committing oneself to faith and good works. In addition, Baptists believe in the separation of church and state and the importance of church service. Note that, in Gilead, religious belief and legality are linked, and no one actually goes to church.

Moreover, Baptists believe that there should be no intermediary between the individual and God. They believe that the individual must go to God directly with their thoughts and prayers, and such a belief does not exist in Gilead. The Commander of each household reads only specific passages of the Bible to the other members of the household (and some of these passages are changed, verses are omitted, etc.), and prayers are not said by individuals but rather purchased, spoken by machines, and printed at Soul Scrolls.

Finally, Baptists believe in salvation by grace through faith.  For Baptists, there is nothing that an individual can do to deserve salvation; one need only accept God's grace by believing in it. In Gilead, however, there is really no discussion of salvation or grace at all; and, if there is any implication of it, it would likely be that salvation is achieved through properly performing one's designated societal role.