The intent is required. Again, it, at the minimum, should be virtual and to do whatever the Church does. If the minister of baptism does not have such an intent, the baptism is invalid. However, it is a very low standard to meet. If, for example, an atheist knows that Catholics in general will always prefer a dying baby be baptized, and that he can, even if he does not believe the first thing of the Catholic faith, but out of respect for that desire, he does baptize the baby if he finds himself the only available human being who can do it. The minimum intention is very well met there, because while he cannot intend the remission of original sin (“intend what the Church intends”, because he doesn’t believe it), he can very easily intend to do whatever it is the Church does: baptize according to the wishes of the parents, who themselves desire a Catholic baptism for their child. He is doing whatever it is the Church has asked of him. He is doing what the Church does, without intending what the Church intends.

Jesus Christ Will Never Allow His Church to Ordain Women to the Priesthood
“I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgment is to be definitiv...