Here’s my background: I spent 10 years working for a government contractor (Lockheed Martin).
Understandably, there were serious concerns about integrating GPL software as part of any deliverable. However, in the case of RawTherapee, in nearly any use case (and definitely yours) it falls into the category of a tool, not a component of a deliverable product.
As a tool - we even had approval to use GPL software (although there needed to be a fairly long approval process that included a security review) in our labs which were processing classified data.
But like Lowell, I feel your pain. I had one situation where we wanted to include OpenSSL as part of a deliverable. The license of OpenSSL happens to be such that it was legal to do this. However, our internal legal compliance team were F**ing lazy and relied on an automated tool that basically grepped the source code for various keywords. The end result of this tool concluded that OpenSSL was under both the actual OpenSSL license and the GPL - because of files in the source code distribution that explicitly called out the GPL as being incompatible and them matching that keyword! It took MONTHS of the engineering team “vehemently disagreeing” with legal before we could get a human in the legal department to actually sit and read the fscking license.
As someone who has a minor contribution (so far, planning on more in the future) to RT and is hence a small-time copyright holder, my interpretation is exactly in line with @heckflosse - Read the license terms, if there is nothing in those terms that is problematic for your use case - go ahead! (In general, for any government user merely using the software as a tool with no modification and no redistribution as a component of a deliverable, there are no problems I would expect).
In fact, the nature of the license is such that even if an RT contributor objected to government use - as the software is licensed under the GPL and thus their contribution is a “derivative work” which falls under the GPL - they could not object to government use as a contributor doing so would violate section 10 of the GPL:
You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.
As a side note to the original poster - the NPS rocks. If any of you use trackpad/touchpad scrolling, I’ll be incredibly proud to have made some of your lives a little easier. 
You’re one of my favorite government agencies!
As a side note, @rangerdavid - are you based in any particular park? One of my college classmates worked for the NPS for years. They are now working for (if I recall correctly) an environmental nonprofit organization. They time as a ranger in Shenandoah and Yosemite, and are now back in the Shenandoah Valley working for the Valley Conservation Council.
So I’d be surprised if RawTherapee, Darktable, GIMP, QGIS, or any Open Source application would be an issue /from a licensing standpoint/. I would think the only issues may be with some managers who don’t understand or “trust” Open Source, confusing it with some of the crappy freeware/shareware out there.
