Should Catholics support "Don't ask, Don't tell?"

My understanding is that the Catholic Church opposes employment discrimination against gays and lesbians unless there is some specific reason why sexual orientation is relevant to a particular position (e.g., priests, in the Church's view).  If I'm mistaken as to this premise, please let me know in the comments.  If I'm correct, then I'd welcome feedback on this short hypo:

Suppose that the U.S. military, in the late 19th and early 20th centuries, had a policy permitting Catholics to serve, but forbidding them from revealing their identity as Catholics.  If their identity became known, they were discharged.  The rationale for the policy is hard to pin down, but usually it centered on the belief that Catholics' presence would undermine morale and compromise military functions because of non-Catholics' reaction to Catholics, particularly in the close quarters of combat.  In other words, the policy was justified based on soldiers' current views of Catholics, even if those views were prejudiced.  Catholics would (and should) have opposed such a policy, even if the open admission of Catholics into the military would have caused some soldiers to react negatively.  Catholics could have bolstered their arguments by pointing to the effective function of other nations' militaries that were open to Catholics.  In time, the inclusion of Catholics would reveal how unnecessary the exclusionary policy was, reducing harmful social prejudice in the process.

Is the current military policy on gays and lesbians different than this hypo?  If so, how?  Should Catholics react to current military policy differently?  If so, why?