It depends.

First, it depends on the size of the pot. I'm a lot more likely to call a river donk in a larger pot than a smaller pot.

Second, it depends on the player. Some players like to take a stab with air, and others will only do it with the goods. I'll tend to call unless I can put them in the "only donks with the goods" category.

I'll tell a funny hand on this subject that I can't start a thread about as it is too low content.
Live $4-8 game. Villian from what I've seen is tight conservative player thus far.

I have on button and raise villian who is MP2. BB calls. Three handed flop.

Flop: Check to me, I bet, they both call.

Turn: Check to me, I bet, SB calls, Villian check-raises, I call, SB calls

River: SB check, Villian bets, I fold, SB folds.

How could I be good here sandwiched between two players with a four flush on the board after that action????

Villian throws down face up and says he was playing his straight draw.

I am not advocating being a POW and this certainly seems like a correct play, but the moral of the story is that making good folds on the river is not the way to make money at limit hold'em.