Thanks for the responses everyone!
Let me clarify a couple of points:
First, the thing that seemed wrong to me was that a non-Catholic was singing half of the psalms that occur between the readings at the Easter vigil Mass. She was at the same lectern where the readings and the Gospel are read, not the stand that is off to the side, where the hymns are led. (My understanding is that the psalms are always to be proclaimed from the place where the other readings are proclaimed.)
Second, I’m not concerned about choir members and organists. There are freqently Protestant choir members. Although I don’t really understand why, from their standpoint, Protestants would want to be members of a Catholic choir (at least if they are unpaid), I’m quite glad they’re with us. And around here, the organist is always paid (even if it may not be much), and it’s much better to have a Protestant organist than no organist.

Anyway, it’s not the same as singing the psalms, which are readings even if they are sung.
I don’t think that there would be anything in the psalms that would be contrary to the beliefs of a Protestant. It just feels wrong to me to have a non-Catholic leading them.
That’s why I’m asking the question. I’m not so much interested in what happens, as what is actually allowed. Lots of things happen that aren’t allowed.
The woman sang very well. She did a great job, and she seems to be a very nice woman. (I don’t know her that well.) But there are several Catholics in the choir who would have been willing and able to do a very creditable job of leading the psalms if it were necessary in order to follow the rules. (Just to make things clear, I am not one of those people. This isn’t that kind of situation at all.

)
If it isn’t supposed to happen, then I would have a very discreet word with the music director. If it doesn’t matter and my “is this correct?” radar is oversensitive, I would be happy to be reassured of that. But it sounds from Mark’s post as if this is not so. If there is anything more specific linking (or of course decoupling) the role of psalmist with the role of lector and indicating that the rules that apply to one apply to the other, that would be helpful. I hadn’t heard of the distinction between cantor and psalmist before, and in my head (not always well connected to the outside world) “psalmist” refers to King David.
Thanks!
–Jen