Two words: School Boards
More accurately, four words: State Boards of Education.
On its own, I don't think that the "RRR" is much of a threat. It's only when they're used by Republican politicians for their own advancement that they're put into a position where they can credibly threaten to twist American into their own image.
At the national legislative level, I agree... perhaps even at the level of state legislatures. But -- public school curricula are not decided by legislators, and amid school boards you can find many painful examples of the RRR exploiting a local dominance of the GOP.