The fact that she was so discreet the only way she was outed was by an obscure reference in obituary. Then fired?. I’m not comfortable with churches, employers or government peeping into people’s private life. Once they start you could be next.
After you publish it in the news paper it really isn’t private anymore.
I am guessing the school suspected that she was a practicing lesbian prior to the obit but after the obit and complaint from a parent they could no longer pretend that they did not know.
There is nothing in the story to indicate that the church "peeped" into her private life. The information was posted in a public newspaper, and brought to the attention of the Diocese by a 3rd party. As a religious employer, if the information revealed a violation of the employment contract on moral grounds, the employer had the right to terminate her employment. If you don't want your employment to be subject to such morals clauses, don't work for a church or other religious employer.
This reminds me of a case a couple of years ago. A single woman who was a teacher at a private Christian school became pregnant out of wedlock. Sexual relations outside of marriage was a violation of the terms of her employment contract, and she was fired. She also tried to sue to get her job back. That was a silly lawsuit as well.