I will be a little contrarian here (but be assured I don't work for United, own stock in United or have any corporate relationship with United).........
I wouldn't condemn a whole airline for what we all know is a USCG perception problem. That agent (and I venture to guess most of the citizens of the U.S.) don't know that much about USCG. So instead of taking away business from them, which won't solve anything, try to inform them. It's worth a shot......
I would formally complain to United via their website at
http://faq.ua2go.com/display/4n/kb/...3S1OA64DwwrR4UyhK6fv2ylkXXS&cid=1&r=0.1268915
You can also get there by going to UAL.com > Customer Service > email us
I would fill out the form AND thank them for their military personnel policies WHICH ARE VOLUNTARY on their part, but would also inform them that according to their CONTRACT OF CARRIAGE, (which is the legal document that does defines their responsibilities), military personnel are defined and that the USCG is a military organization under their definition just like the USN, USAF, USA and USMC, and that you hope problem can be rectified.
It will interesting to hear their response...and who knows, you might end up educating not only a gate agent at LAX, but maybe a whole airline!