You're in a difficult position and there aren't a lot of good options here. Your adivsor is wrong to have put you in this situation. From an ethical perspective, I think it would be wrong to have your supervisor as an author on this paper. On the other hand, you also clearly feel that you have no choice in the matter and feel that standing up to your advisor on this issue is not worth the trouble it would cause. Ultimately, that is your decision to make.
The best course at this point is to set up an honest conversation with your collaborator. I would do it over the phone or video chat. Explain the situation clearly and completely (just as you have here) and explain that you feel like you've been put into a difficult situation.
If your collaborator is also uncomfortable and is willing to be the "bad guy" by going on record as putting their foot down on the ethical issue of authorship (even if they are more open to the possibility than that), you might have a solution.
In that case, you can go back to your advisor and say that you asked your collaborator to put their name on the paper and that your collaborator pointed out that according to their university's and/or funder's rules and/or their own personal convictions, they felt that it would be wrong. The policies and rules bit is almost always true because basically all rules on these subjects say that co-authorship in these situations is wrong. Tell your advisor that you did your best but you could not get your collaborator to budge on the issue. Your advisor may be mad, but they won't be mad at you.
If your collaborator is not willing to potentially annoy your advisor, an in-person conversation will at least allow you to make it clear that you're not comfortable with the situation either. At that point, the two of you will have to decide what to do.
I'm sorry you've been put into a such a tricky place.