Democrats do actually enjoy an edge on education, at least in red states. Many voters trust the GOP government to stop 'CRT' but want to stop them from defunding public schools. For instance, Indiana had a Democratic suuperintendent quite recently.
Sherri Ybarra, Idaho's incumbent Republican Superintendent, only won reelection by 3% in 2018 against Cindy Wilson. That's a very good example of this. Education has traditionally been a Democratic issue, although that advantage has been lessened in recent years because of the fights over CRT, teachers unions, and the coronavirus pandemic.