As of today, May 31st, it appears that many states are opening up their state park campgrounds. Most, however, are only doing it at 50% capacity. Some have restroom and shower facilities open, others have not. Some have abandoned their reservation systems entirely, in order to control the number of campers when at the gate.
National forest and park campgrounds are very slowly being opened up, but a few will stay closed through 2020. Some national parks will have limited services open, such as general stores, delis, fuel stations, and restaurants.
It would be wise for campers to check the websites of any campgrounds they are considering, for the status, before departing from home and then again when en-route.
This thread will be updated as needed.