School me in public parks camping...

United States Forest Service campgrounds in Montana rarely accept reservations. There are a few near Red Lodge, MT that do, but they also have some sites set aside for first come, first served. Most FS campgrounds have vault or pit toilets, and one water faucet for each 5 sites. A "water thief" can not be used on most of those faucets; you will not be able to hook up a hose. There is no electricity. Most campgrounds do not have dump stations. In fact, the nearest dump station can be many miles away. Conservation of water is a way of life! Very few campgrounds will allow emptying your RV tanks into the vault toilets.

This is a very good guide to National Forest Campgrounds:

https://www.forestcamping.com/dow/list/nflist.htm