Came back to this thread to find pages and pages and pages added...
On the issue of schools teaching critical thinking, including the subset of it that is the scientific method:
I think we distort this if we treat is as a simple yes/no question, do they or don't they. I think the question is
how much they teach it, crowded in among all the many other mandates teachers have. There's an immense amount of "schools should teach this, schools should teach that" out there and it results in curriculum standards that look great on paper but only leave a teacher room to squeeze one day in, maybe, on a particular topic or skill.
My university has a social studies education major, and our new coordinator has worked really hard to make that program prepare our students for all the demands of the state praxis exam. That means history, sociology, anthropology, political science, economics, and geography, apart from the courses they need on various aspects of pedagogy. Shoehorning all that into a major that can be completed in four years is really difficult. You know those stupid memes that run, "Instead of algebra, schools should teach kids how to balance a checkbook and fill out a tax return" blah blah blah? Actually, all that stuff IS already in the state standards, here in NH at least - it's listed under "economics" and is the responsibility of the social studies teacher... who is also supposed to teach history, and civics, and geography, and... you get the picture.
The other thing is a point I would draw from religious circles I listen in, but I think has a wider application, including to educators. That's a realistic sense of proportion of the inputs in people's perceptions and thinking. What I mean is, a pastor in a church gets twenty minutes, maybe 45 at the outside from a really supportive congregation, to preach a message to them, once a week. Then those people they spoke to for 20 minutes go out and listen to the radio and watch TV and scroll through social media and youtube videos - for hours and hours and hours, every day. Just on the numbers, the odds of that preacher's message significantly impacting people's thinking, relative to the constant barrage they face from mass media, are pretty slim. Of course, you can take to mass media yourself, but then you will only gain profile if you play by mass media's rules, which may themselves negate the message you're trying to send. The medium is the message and all that.
I think something similar applies to schools. K-12 schools have the kids in the building for something like 30-35 hours a week, maybe. But for the most part that time is divided between 6-8 different classes and teachers, plus lunch and gym and study halls, so any given teacher is getting maybe 4-5 hours a week max with the kids. More opportunity for influence than a preacher's 20 minutes, but still only a sliver of the total attention. College classes take 15-16 hours a week in the classroom and then expect (rather desperately) that the 19-year-olds are devoting lots of hours independently to doing the readings and writing papers and all. Again, any given prof gets 3-4 hours a week with a kid. Put that up against the 24/7 availability of social media, that's purposefully engineered for the sole purpose of capturing attention, and you see the uphill battle.
I think what we're missing in the "schools should teach critical thinking" thing is that, chances are, they ARE. But there's a difference between the teacher teaching it, and the student learning it. It's just that the time the teacher gets to present it is swallowed up in the much bigger world of the student's attention, while inputs contrary to critical thinking are much more dominant.
I have been in schools my whole life (well, since I was 5 years old anyway). I would not entrust any school to teach non-biased critical thinking. There are many teachers who could do it, but there are just as many with an agenda that would infiltrate the process. I see this every day at the university. For every professor providing a forum fro open-minded evidence-based inquiry, there's another who is blatantly indoctrinating students with their biased world view.
I can think of a former colleague who matches your description pretty well, of a professor who had an overt agenda and saw her vocation as inculcating it in her students. However, the main reason that I'm aware she was like that, is that I periodically heard complaints from students about her being like that... which implies that, again, there's a gap between what the teacher is teaching and what the students are learning (or indoctrinating, in this case). It seems to me that when a student comes into a class with a sharply different worldview from a doctrinaire professor like that, 99% of the time they don't get indoctrinated, they learn techniques for "surviving" a class with a doctrinaire professor - or pass information around to other students so as to avoid that professor's classes if possible - and then carry on as they were. The experience leaves a bitter taste in their mouths that may have the opposite effect of what the prof hoped for.
I think in reality, what happens in colleges is that students tend to congregate around professors they see as mentors for interests
they already have. If the student is inclined to one worldview or ideology, they'll figure out which professors support that view and take as many classes from them as possible, and if they figure out a professor pushes a contradictory ideology, they'll avoid them or, if that's impossible, grit their teeth and "survive" that person's classes. It may look like indoctrination when one sees the troupe of fans of some very ideological prof, and it may be a shock to the kids' families if they hadn't known what their kid was thinking privately and not communicating before, but in my experience it's pretty rare that a college student radically changes their whole worldview because of a class they took.