This looks like one of those studies designed to try and get one over on the church. I’m sure the researchers are not all so concerned about the health of a few thousand nuns.

There are plenty of other women who happen to never become pregnant and who don’t take the pill and I don’t see them all agitated about them.
I don’t think it’s a study designed to try and get one over on the Church, at least not if they know anything about the teachings of the Church. The teachings say that artificial birth control is forbidden to prevent conception. However, contraceptives are allowed if it’s to treat a medical condition. Nuns are celibate, so them taking contraceptives for health reasons is a non-issue to begin with. Therefore, if a nun, for fear of uterine cancer for whatever reason is going on with her, takes contraceptives for the perceived health benefits, and that is
why she is taking them, she would not be sinning to do so.
Should a nun take the pill for health reasons? I’m not certain. It’s true that the pill raises one’s chances of some types of cancer (and has a host of other side effects), but it
is true that it lowers the chances of other cancers. How people direct their health care is personal, so only each individual person can determine the course of their healthcare and make their decisions accordingly. The important part is that she would not be sinning in making this decisions, as long as she’s not trying to avoid conception. Clearly a nun taking the pill to avoid uterine cancer (there’s a reason why there’s less uterine cancer afterall) is not sinning by doing so. But by doing so, she will raise her chances of getting other cancers.
At one point in my life when I was younger, I considered taking birth control pills for the lessened chances of uterine cancer. I was single, not dating anyone. I decided against it because I weighed the benefits and risks. But I certainly could understand someone choosing to take them if, for example, they have a history of uterine cancer in their family.