But there is a difference between finding out that the little grey alien is gay, and finding out that your coworker with whom you shower is gay.

Now, I do think that the screening mostly eliminates the chance that Ford would be aggressively homophobic. I doubt that he would even report another soldier. But I do think that he might a) slip up and blab to someone else b) no longer treat a friend as such c) attempt to 'save' a friend.