What you teach is very different from how you interact with your students. I would keep the two separate… meaning if you’re teaching critical thinking, keep it focused on the topics the course is about, not about the student-teacher interaction or ideologies that come into the classroom.
I feel there is an underlying fear in your writing which can become a block from being able engage effectively when you confront the conservatism that frightens you. It will block you because you’re defending yourself, and by defending you are attacked — not sure that makes sense, but quite often what is needed most is careful listening and understanding. Most people just want to be heard, and to feel like their viewpoint has been acknowledged.
It comes across a bit as if you yourself don’t want to admit any personal failings in your teaching methods, afraid that their views and mob mentality may gang up on you. (I like Benjamin Zander’s concept of Being the Board, from the Art of Possibility, as a way of turning that around). You could, for example, change this around by inviting the students for feedback on what you can improve so that they get the most out of the class.
If you’re applying the Socratic method, then you’re already guiding students to their own conclusions through your questioning, which is much less confrontational. But you can make that much more effective with more active listening — acknowledging the belief, and even the origin of the belief, and doing so with compassion and understanding instead the need for them to arrive at a different conclusion.