Refusing a research project and/or assignment because of personal convictions

Standard IANAL disclaimer (I’m speaking from anecdotal experience and could be very wrong).

I had a student who recently refused to work on a political dataset because of her political views. I could’ve told her that this was a material part of our work and she has to do it or I can’t advise her. I don’t think there would’ve been any repercussions to me if I did. Generally speaking, if an advisor doesn’t want a student the reasons why aren’t very relevant, it’s best to part ways.

Eventually I chose not to and assigned her to another project. Did her academic progress suffer as a result? Sure. She made a choice and is paying some price for it.

For funding/collaboration, I can hardly see what legal protections could exist. If you choose not to apply for a DARPA grant or work with anyone there, you can’t reasonably argue any grievance as a result. Say, if you’re up for tenure, saying that you didn’t secure any funding but that’s only because you refuse to work with DARPA sounds preposterous.

A similar case goes for boycott movements (e.g. BDS). My field (computer science) has a very strong Israeli presence; if you’re a BDS supporter it may limit your future academic prospects. No one can force you to collaborate with Israelis, but in some cases, it may become very difficult.

In the end, nothing in life is free, and you need to decide how important are your personal convictions vs the price of following them.

Is there a general rule about what a postdoc or graduate student can or cannot refuse to do because of personal convictions?

I'm not a lawyer, but anyway I doubt many countries would have laws for this. If anything, I think this is more a matter of institution policy.

First, it's important for a person to be hired as postdoc or as a PhD student to do their due diligence: they are supposed to know what can reasonably be asked from them before signing the contract. If some of it challenges their personal convictions, they should discuss it beforehand with the PI and warn them about what they don't want to do. The PI might end up hiring somebody else instead, but this is a risk to accept.

In the case where the conflict between the personal ethics and the job was not foreseeable, the first thing to do is (again) to discuss it with the PI: they are likely to understand the objection and often find an alternative option.

But if there is no agreement at this level, then it has to be settled by the institution procedures. This would completely depend on the institution policy and the nature of the moral objection, obviously. In general I assume that the institution would try to find a compromise satisfying for everyone, for instance by assigning the person on another project. However it's worth mentioning that most academic institutions have ethics committees in place. My intuition would be that if the study requiring the task objected to was granted approval by the ethics committee (as it should have), then the institution would be entitled to ask the person to perform the task or quit the job.