I agree with your statement.

 One thing I don't know about the transgender is about the hormones they take - do they have to take them daily? What happens to their physical and mental state if they have to go without them for a long time?

If a person is dependent on drugs to maintain physicality or mentality, generally they are not considered fit for military service. Banning transgenders is likely more about their fitness for active duty than anything else, (although unit cohesion, especially in combat troops is critical for success).

Not being fit for active duty would be a disqualifier under the merit category.