1: Using the site as a credit card validator. Only the real ones will get through.
2: By making donations to places with a stolen credit card little bits at a time, it establishes a wider pattern of use for that card. Fast forward a couple steps ahead, the purchases are getting a little weirder each time, and before you know it, you're at whatever level people use stolen cards to buy.
3: Tiny non-profits generally do not have a great deal of extra man-power to deal with such things, and there's a better chance that this sort of behavior goes unnoticed.
4: When people see weird charges on their card, some people are more likely to feel bad enough taking away money from a non-profit organization that they won't report the abuse, or they may not question it if the card is joint-used.
I'm sorry that I don't have sources on these, the research was from a couple of months ago. It's pretty frustrating and there seems to be little retribution for things. You have to just change your charge flow and move on. :/