I've seen something like this myself, but I agree with Tordmor about what it is.

In my engineering degree, we had to take some "liberal studies" courses to complement the technical stuff. In one of these we had an irrationalist as a teacher. She would state crazy beliefs like that homeopathy was just as legitimate as "western" medicine, different cultures have different truths, and that science doesn't work in some cultures. Naturally, I challenged some of these ideas, but the response was to just shut down criticism and dodge questions "who's science?", "yes that may be your view, but we are talking about this guy", and so on. I didn't want to just irritate everyone and disrupt the class indefinitely, so the teacher could just ignore criticism until it went away.

At this point we were all strong technical thinkers, so it was very frustrating for everyone, tho everyone else was much more shy about calling out teachers than I. We eventually decided on a model of what was going on: we were being presented with incoherent "facts" that we were forced to memorize and were not allowed to criticize. It was practically a recipe for brainwashing. What it felt like was undermining the precision of thought that we had trained as engineers. It felt like my brain would turn to mush by being forced to integrate these incorrect bits of knowledge.

I don't think that terrible feeling was the result of a clash of memes from opposing belief systems. Engineering is not a belief system; it is a precise art that requires precise thought. It felt like being forced to use your nicely sharpened tools on a task that would destroy them.

So I think that when you notice that feeling, you should stand up for the sanctity of your mind. Even listening to that stuff puts gunk in your gears. You should have called the guy out (politely) for depriving people of the ability to help each other reach a better understanding of things.

Communication must be two-way to be useful. If you disallow criticism, so that only agreement is allowed, the communication ceases to be interactive. You lose the ability to discuss an idea before accepting or rejecting it.