This is really the same argument, so I am going to address them together.
There are a great many things in the field of social studies that are inherently controversial. World-renowned historians argue over all sorts of things because they don't agree. So to the extent you do not want "different versions of World History" to be taught in different states, you are asking someone at the national level to decide - for the entire country - which views are correct, and which are not. That is inherent in wanting that decision centralized. And that is true in all sorts of other fields as well
How much focus should we put on Europe v. Africa v. Asia v. The Pre-Colombian Americas? Which cultures are we going to study, and how are we going to view colonialism, capitalism, communism, socialism, etc.? Should we focus less on dead white people and more on people of color? Was "Manifest Destiny" good or bad? Should we teach about the "patriarchy"? Is teaching English lit too eurocentric, and should students be required instead to read other things instead? What are we going to teach about gender, and gender roles, etc.?
These are inherently controversial topics, and we know that because parents, school boards and educators fight about that stuff right now, all the time. Those disagreements won't vanish just because the decisions are centralized in Washington and mandated to the states.
That's not accusing left-leaning teachers or educators of trying to deliberately brainwash students politically. They are pushing for the curriculum they honstly believe is the right one to teach, just as are those who disagree.
So, it shouldn't come as much of a surprise, or even as an insult, that does who don't lean left would prefer that those decisions not be made by an admittedly left-leaning educational establishment.