Yes. The Catholic Health Association has issued a public statement that indicates they find nothing morally prohibitive with the Pfizer or Moderna vaccines. The position of the Catholic Church is that, in general, vaccines are a moral good preventing disease and saving the lives of millions of people.
The Pfizer and Moderna vaccines were not developed using cell lines from aborted fetuses. Therefore, both vaccines are morally appropriate to distribute by Catholic health care organizations, including all CHRISTUS Health ministries.
The Oxford-AstraZeneca vaccine and others developed using fetal cell lines are morally appropriate to use when there is no alternative available. This is because a critical moral issue regarding vaccines in Catholic theology involves the use of cell lines from voluntary aborted fetuses in their development. The Moral Reflection on Vaccines published by the Pontifical Academy for Life suggests that vaccines using these fetal cell lines should be avoided and alternatives should be sought. The document goes on to state, however, that in the case where no alternative vaccine is available, the use of existing vaccine is morally acceptable.