What should you do if a co-author has an unethical affiliation?

To my mind, this case is very similar to the question of whether somebody can essentially pay for co-authorship. We see many questions of this sort on this site, a particular apropos example of which is this one, which asks in part:

Suppose I'm a billionaire who knows nothing about science, but I take it into my head that I want to be (regarded as) a famous scientist.

The case of the Saudi Arabian affiliations looks to me very much like a parallel construct:

Suppose I'm a billionaire institution which does little significant research, but I take it into my head that I want to be (regarded as) a famous institution.

I think that it is completely reasonable to find this problematic, and to object to a co-author adding this institution, just as one might object to a co-author adding the billionaire know-nothing as another author.

Now the question is what to do about it, and, as in these authorship questions, the advice tends to depend strongly on the power dynamics of the situation. On this site, we often advise students to leave bad situations rather than creating a confrontation, due to the power imbalance with faculty. For people in positions of power, however, like tenured faculty, it is an effective endorsement of unethical behavior if you are aware of it and do not call it out. It may not be a hill to die on, but either you care enough to make your voice heard or else you accept the behavior as legitimate.

In this particular case, the student may have acted unwisely with regards to safeguarding their own future, but it may also have been important enough to them to take that ethical stand. It's impossible for us to know how important it was to that person, and it's easy to engage in post-facto critique of their tactics, but I think the concern is legitimate and the actions taken are within the range of reasonable options, depending on how strongly the student felt about the ethics involved.

In short: some people choose not to take military money, not to work on espionage-related research, or not to publish in non-open journals. Choosing not to be party to what you perceive as bribery for prestige is just as legitimate an ethical choice to make.

One unwritten rule of any scientific collaboration between co-authors is that each party should trust the other. If I collaborate on one paper with another scientist (who might be located in another part of the world) and he is affiliated with more than one institutions (e.g., a university and a research institute or a second university while on sabbatical) and tells me that he likes his affiliation on this specific paper to be "Institute A" or "Institute B" I trust that he is doing the right thing. When he wants me to add an acknowledgement about a specific grant, I put the acknowledgement he wants for HIS part and I put the acknowledgement for my grant that I want. I have never felt the need to question neither the grant acknowledgement or the affiliation of another collaborator. For me, it is always a matter of trust. I do not collaborate with people I do not trust and I trust the people I collaborate with.

On my CS domain, where conferences are the main publishing venue, sometimes the affiliation or the grant explicitly written on a paper, sometimes corresponds to who or how the trip expenses of the suggested paper will be covered. In those cases, the author may have prior discussed this with the administrative division of his institute and only follows the provided instructions. Again, I have never thought of any of this as a big deal, because it is more of a administrative technicality than a real issue.

As far as the OP original question, her advisor wanted to list both affiliations (not just the "shady" one). In my mind, this was really not a big thing. Instead the OP by escalating this issue, was basically forced to resign from her PhD. And all this for what? So that a small obscure university has one less citation? It makes no sense and there are much more important ethical fights that is worth fighting for within Academia.

It would be a whole different story though, if the OP was forced to put another affiliation for herself. In that case, she should have a saying on which is her preferred affiliation. But fighting for the listed affiliation on another co-author makes absolutely no sense to me.

Withdraw from the collaboration.

Certainly, she cannot insist that the other author breach his contractual arrangement or indeed disregard his own reasonable view on where he is affiliated merely because she is unhappy in how the affiliation arose.

If his view on where he was affiliated was essentially a fiction of his own invention, I think, it would be reasonable to take a robust position against perpetuating a fiction or a fraud. But that is not, from what I understand of the question, what has happened here. If he is paid by the university in some academic capacity related to the paper, for whatever reason and for whatever work is delivered, then I believe he is entitled to assert that he is "affiliated" with that university when publishing the paper. And the university may well require him to make that assertion. It is no less reasonable than a grant body asking to be acknowledged when work is produced from a grant.

If that is too much for her to tolerate, then the cost of having that kind of ethical standard is to withdraw from the collaboration and desist in publishing the paper: ethics would be worthless if they had no cost to their subscribers.

I have to add, when I read the title I thought the question would concern a proposed affiliation with an ISIS or Al-Qaedea subgroup, or at least with a supplier of arms technology to a capricious dictator.

Frankly, to get upset that a university in a developing country has to promote itself against the entrenched western universities by retaining (effectively) a consultant on their payroll, is bordering on the absurd. There are many problems in the world and many problems in academia. Saudi Arabia throwing some money at a small number of professors is not one of them.