I often feel as though the people I engage with are completely unwilling or perhaps unable to actually change their opinions, barring some miraculous change in their thinking. is that accurate?

What you're identifying is people whose beliefs have a name rather than people who have a belief as an identity.

For instance, the things that I believe are termed "anarchism." I didn't go out, read about anarchism, and decide that sounded like a good thing to believe. If somehow a core tenant of anarchism became "it's ok to hurt kids," I wouldn't sit there and try and justify why that makes sense actually or that it's fine, I would believe something else.

If people's beliefs are resistant to change it's because you're encountering their most basic, core beliefs as exemplified by a professed belief. You can't change people's core beliefs through argument, not quickly anyways.

You're right, I'm generally not willing to change my core beliefs as a person based on one interaction.

I'm not going to say that's completely impossible because maybe someone has thought of some devastating argument that I've literally never heard before that could make my world crumble in an instant. I'm not putting that out of the realm of philosophical possibility.

But if there was some point or some argument that could undermine those beliefs, I would have already applied that to what I believe and I would believe something else.

People act on the synthesis of the best information that they have available to them at the time but it's bad thinking to say "I'm going to change your beliefs by giving you better information."