If two same sex SMs with opposite gender IDs can share a room, why can't two opposite sex heterosexuals?

Don't ask, Don't Tell has been gone a few years. Sex reassignment paid for by our tax dollars is in the works. We're still far from the clear of equality though. A soldier asked me today why he couldn't be roommates with his girlfriend in the barracks (same company). I replied with the standard its against policy such and such. He then pointed out that two individuals of the same sex whom are in a relationship are roommates and wanted to know if this would be grounds for an EO complaint.

I opened this up as a general discussion between all the troops. I've reviewed 600-20. By the definition of EO allowing SM that self identify as LGBT to be roommates with individuals of the same sex and not allowing heterosexual individuals of opposite sex to share a room is discrimination based on sex and gender preference. However, deleting policies that require segregation based on sex requires a civilization that has grown accustom to these ideals. Do you think America is ready?

I've lived overseas a large portion of my life and served with our Allie nations. Men and Women sharing restrooms, billeting and even bathing facilities is common in many places. Especially when it comes to the military's in these countries. Do you think our military is mature enough to handle such a change?