We volunteer with Habitat for Humanity both at our local affiliate and with affiliates around the country via their RV Care-A-Vanner program. We have never been charged to volunteer. They do background checks, they provide safety training, provide hard hats, etc.
I guess I "pay" because I bought some steel-toe shoes, gloves, and tools and some specialty items that I prefer using on construction sites. Other than the steel-toe shoes (which are not required), Habitat provides everything else. I simply chose to purchase some items that I like better than the standard issue offered by Habitat. We also "pay" in the sense that we travel in our RV at our expense. However, the costs specifically associated with Habitat can be deducted on taxes if you itemize.
I can imagine that some organizations need help offsetting expenses.