Chad, that is illegal. Soldiers assigned to Fort Bliss, or any other DOD post are allowed to maintain our 2nd Amendment rights unless there is official, legal disciplinary action to the contrary (such as an actual court-martial) as long as we are off-post and operating within the laws of the state (Texas). The exception is on-post or on federal land, due to command policies. Any orders to the contrary are in violation of Congress and should politely be treated as such- you can simply reference the Act and let your CO read away. If he keeps on it, go over his head and contact IG.
Furthermore, if you are forced to surrender your firearms, DO NOT turn them in to your unit. Family, the Rod and Gun Club, or the MP armory are ALL preferable to your unit arms room.
Registration is the worst option, and according to the Act, it is no longer mandatory. A lot of our leaders are trying to 'look out for us' by violating the rights that we do have, and it pisses me off, and that's why I'm leaving. To me, NCO is just another way to say "incompetent, power-hungry, slacker", but that's the caliber of leadership we have in 3-41 Infantry.
Get out and work a real job and don't tell the government about your legally-owned weapons. Registration precedes confiscation- just ask Australians!