One can never be absolutely certain how this will turn out, but we do know that the big guy in DC wants to discontinue business closures as soon as we see a decent decline from the peak. Therefore it seems very plausible to assume that national parks will be open during most of the summer. And we can assume that many people will feel spooked about traveling (witness the vehement reactions to suggestions that restrictions might be lifted by summertime), but some will not be scared and will go camping (witness the optimism of others who feel this is somewhat overblown).
If I were to guess, it feels to me like business volume for your park may be down to 40% or 50% of normal. If this will provide enough revenue to justify staying open, then stay open. If you close for the year and it turns out you didn't need to, you'll kick yourself for years to come. If you stay open and wind up having a dismal, money-losing year, it might still be less of a loss than if you'd closed.
As for the public safety aspect, people will do what they are going to do whether you're open or not. If they want to camp, they'll camp with you or (if you're closed) with a competitor.
Of course, make sure your liability insurance stays paid up and in force. ;)
