Apologies. I am not a Catholic, so I may not understand who is and is not permitted to be an employee of a Catholic university, still less one in the US, which will have completely different employment laws. However, it does not seem that he would be teaching Catholic moral theology, so I am not sure whether his views on topics in Catholic moral theology are relevant. Pete Buttigieg is clearly a very intelligent man, a graduate of Harvard and Oxford, with experience of the private sector as well as careers in naval intelligence and politics, and he is only 38! He seems to be more than qualified for the position. I couldn’t comment on whether his views on various policy issues make him unsuitable to hold a position at a Catholic institution.