Maybe it just means that we need to ensure politically proportionate representation when it comes to teachers, and have the conversations flow naturally with a balance. Maybe it means that we have to specifically put down rules for teachers to no delve into any political/ideological topics/opinions and to only teach the subject matter. That one would be a good start, and it's not immediately obvious that it would be indoctrination of children.
1. What is the teacher's take on students making errors - Do they immediately correct them? Do they give the student the time to come to a contradiction themselves, but possibly confuse them and other students? Something else?
2. What is the teacher's take on mathematical knowledge - is it there to be discovered, or to be created? How much of math is already known by academics and how much is still in the future? Do they teach concepts as fully given, or as challenges for the students?
Each of these and many other aspects of teaching could influence the student's view of authority and their own agency.
There are still people today in the US who consider teaching evolution a step too far. In the US one of the major parties considers modern climate science off limits because they disagreed with its conclusions.
Then you get into history and literature and it’s almost impossible for politics to not influence what should be taught and how it should be taught. Yes, the teachers should still primarily be trying to impart kids with the tools to analyze things and seek knowledge themselves, but some topics are just too human to believe that they can be taught from a completely apolitical perspective.
This pattern of people leveraging their professional position as a platform for activism is questionable, but debatable, in general. But being entrusted to teach children requires exactly that, trust. If school systems lose the trust of parents, and eventually their larger communities, they're done.
If schools can be reasonably viewed as attempting to indoctrinate children, there will be a massive backlash. People will put up with a lot, but their children are generally off limits.