Remember that from a Catholic point of view, a female Methodist pastor can baptize validly. Baptism with water, in the name of the Trinity, with the intention of following the Great Commission.
True, and a female nurse (or anybody else, for that matter) can also baptize validly.
The problem is that when a Successor of the Apostles subjugates himself to a female minister, the picture transmits the message to the average person that the cardinal and the female minister are at the very least interchangeable.