I have mixed opinions on this. As you cited Houston Methodist, I wonder how short they are on nursing staff? It looks like they dropped 151 hospital workers, while giving some 600 employees exceptions (out of maybe 22,000 employees across eight hospitals).
On a purely utilitarian basis if the nursing shortage is too severe it may not be worth it to fire unvaccinated nurses; with proper PPE and regular testing the risk of an unvaccinated nurse spreading the disease may be less than the risk of a facility being unable to save a patient due to lack of staff. The fact that there are hundreds of staff exempt from the rule - more than those fired for noncompliance - indicates that the hospital is confident in their ability to provide care even when an employee is unvaccinated.
I will copy something from the breaking news thread,
~Max