Found this on Facebook:

Mt. Whitney Portal Campground
Originally Posted By: Mt. Whitney Portal Campground
Whitney Portal Road, Lone Pine, California 93545
(760) 937-6070


September 29 via mobile
Hello Everyone just to let all of you know that the Federal Government Shut - down will not impact our operations we will conduct business as usual. We will leave the camping,fishing & hiking up to you lol just remember it is cool at Night up at Whitney so bring your cold weather gear.

Richard R:
The reservation web site is down as well. How can we find out if there are any camp sites available?
Campground:
Mt. Whitney Portal Campground OPEN,OPEN,OPEN are we all Campgrounds open up here in the INYO'S so keep coming


I believe the campground hosts are unpaid volunteers, so they are still operating.