It is implied that the Church stands against science. The opposite is true and many great scientists were also priests, e.g. Nicolaus Copernicus (Poland) or Gregor Mendel (Czech). Saint Augustine stated already in the 4th century that faith and science are equally important and Pope John Paul II wrote: "Faith and reason are like two wings on which the human spirit rises to the contemplation of truth."
In the very beginning Ava had the Halo put inside her because it was told humans hide it. Although it was not made what or who from.
But then she is at the OCS headquarters where she is wearing a vest to shield the halo from being smelled by the demon . The vest covers the side and front but not the sides which are exposed so it would not work.
The nuns show poor safety practices on their outside training yard. Handguns are aimed at targets while other nuns are training behind those targets.