Diverging coauthor opinions - publish anonymously or don't publish at all?

Rather than knowing that some opinions expressed are contrary to my own views, you could present both views and clearly label them as such. For instance, you could open by explaining:

The authors opinions differ significantly and each author presents their own opinion below:

Followed by each opinion:

Author Name A: ...

Author Name B: ...

You haven't specified your field of study. I think the answer may depend heavily on whether you are in humanities vs. soft sciences vs. hard sciences. I will give an answer from the "hard" end of the spectrum: I work in applied mathematics.

If I didn't agree with the contents of a paper in a substantial way, I would certainly not consent to be an author of the paper. Authorship implies a belief in the correctness of what is written. I would go with option #1.

If I disagreed with coauthors over minor, subjective points (and this happens) I would work with them to find a way of presenting things that we can both agree on. In math, this often means simply leaving out speculative remarks.

If your coauthor is not willing to somehow present the two sides of this coin as suggested by @user2768 -- which is usually the case -- I suggest you go with option (2).

You can always go back to that point to re-discuss the matter on your own, and there's always the chance you will see things a bit differently later, especially once this conflict of interests cools down.

Your career is potentially long, you're probably still young by now and thus prone to overestimate the future influence of a single short publication. Likely not many peers will read it as keenly as you expect, and even fewer will judge you for its contents (unfortunately this is how modern academia is).

Back off now, come back to this later. Good luck!