Catholic institutions (and those of other religions) should never have been employing people who do not believe the Faith, completely and without dissent. If they can’t find enough such people to fill the jobs, then they obviously have failed as a religious body, and need to get out of every other line of work except evangelizing their own “faithful.”
You think every Catholic institution should hire only Catholics? A hospital should refuse to hire the very best surgeon cause he’s Presbyterian or a charity the best accountant cause he’s Jewish?