So far as I am aware, the Church does not take a position on whether women should serve in the military or in public protection capacities. It is in the realm of prudential judgment. If a woman does not have responsibilities to a family, there does not appear to be any reason she could not serve, so long as she understands and accepts the unique dangers she faces as a female military officer, police officer, or firefighter. If she does have family responsibilities, those should be carefully weighed into the decision-making process with the understanding that her family is her primary obligation.
And, of course, all of this applies to men, as well.
