Charities send mail because it helps them raise money, and it's one place that direct mail still works, and it works well. You can call the org and have them take you off their mailing list. I would just ask that if you do, also set up a recurring donation. One time donations are nice, recurring donations are better.
But if you're more comfortable giving Facebook more data about you (donations contain a lot of information) but not giving that data to the charity, why are you donating to them in the first place?