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This question is a splinter of an earlier question, posted separately upon advice from commenters.

The background is:

(1) I audited a course at an institute I don't belong to. As part of the course, an essay is being written by two of us.

(2) There is a chance that this essay would be published either internally or externally (not necessarily peer-reviewed).

The problem:

My co-author and I differ (significantly) on certain areas we write about. In a sense, we represent opposite ends of the spectrum. My partner is keen to publish; I am ambivalent.

I'm bothered by questions of academic integrity, namely:

(1) Do I withdraw entirely, allowing a one-sided, uncontested opinion to be expressed? This is the easiest option.

(2) Do we submit normally, with our names and affiliations, knowing that some opinions expressed are contrary to my own views, and may negatively impact my academic work at a later stage? While uncomfortable, this does seem fair.

(3) Do I remain anonymous, with the partner being the first author? This way we can address the divergence and bring out a contrast in perspectives, without me having to worry about long-term consequences. But I don't know if it is an accepted practice. I have come across questions on anonymity here and here, but these primarily discuss single-author work.

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!

After looking at your previous post, I can't help but see this a bit differently. Unless the assignment had additional parameters about coming together around a controversial idea, and or the "challenge" is to merge your individual authorships into a singular voice, it kind of sounds like your over thinking it. It's not coincidental that you were put in random pairs, with a divisive theme/assignment. It seems like your anxiety over authorship differences, is not only going to be expected, but, it's kind of the point, yeah?

Sorry if i'm misunderstanding something, I just see the assignment as an opportunity to embrace the divide and embrace your differences. As far as precedent, make a new one. You can use subtle differences or typographic changes to refer to different voices. A communicatory battle to show the divide, to persuade your case, or to come together around universal ideas, or drastically break apart for the benefit of the reader, and so on. Maybe it's written from a legal guise, 2 sided, jury/reader persuasion. Maybe it's presented as 2 friends having a casual conversation, and finding ways to unify and come together around drastically different viewpoints.

Whatever it is, it sounds like it was designed to be that way, so I would embrace that, use it, and design/format/present it, in a way that doesn't hide from the divide and adds clarity for the reader.