I worked for chaplains for 20 years. Trust me, no matter who gives what "order" - it is not a legal order and the chaplains who object to this will not be forced to perform these ceremonies.
Chaplains could determine who they married even before this. The only people this is going to affect will the the chaplain's assistants who will have to come in on Saturday to watch Mary Mullet and Betty Birkenstock get married in the base chapel.
Although the chaplains have been and will continue to be allowed to determine who they marry, the base chapel will be used to perform these "marriages".
What will be funny is to see Mary and Betty ask for counseling after one of them cheats on the other & the fight over base housing!