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.
bump
it wasn’t private