Our concession operations on Federal lands are still mostly open today (we had two US Forest Service local offices ask us to close, but these are both offices that have a tradition of interpreting the rules in odd ways).
By all the rules, being open to the public is the right decision. We are tenants on US Forest Service land and operate entirely outside of the government budget, receiving no money from the government and we employ no government workers. No government employee has a duty station in any of the parks we operate. There is no more reason to close our operations than to, say, ban cars from Federal highways during a shutdown.
However, apparently we have been told by several local folks in the Forest Service that the higher ups (this tends to mean folks up in the Administration) are re-evaluating our status. I do not know what is going on today, but in the past this has often meant that the administration is considering closing us to make the government closure as painful as possible. After all, as I have written here and here, parks closures seem to be one of the few things anyone notices in a government shut down.
Update: Our most recent guidance: "1. The Forest Service is allowing concessionaires to continue to operate as long as no Forest Service personnel is needed to ensure safety." It looks like we may have to close a few sites that are dependent on USFS operated water systems, but otherwise most of our locations will be open. I am hoping to get out a press release and update our web site but things are still fluid this morning.
Update #2: Definitely still open everywhere but in one location (Laguna Mountain, CA) where we depend on a USFS-operated water system that will close. no closure press release 2013