The Catholic Faith is not the personal property of the Pope nor his plaything. Therefore, there is precious little the new pope can change about it. He cannot, for instance, alter the matter of the sacraments (that is, the stuff the used to celebrate sacraments) in order to make the sacraments more “relevant”. The Church’s job is to hand down the faith and practice of Jesus and the apostles. So even though milk and cookies are really quite nicer tasting than those flat little disks of unleavened flour and not terribly good wine, the Pope can’t decree that the matter of the Eucharist will henceforth be milk and cookies, even if the People of God think that would be nifty.
In the same way, though lots of people thinks Shea butter is waaaay nicer than olive oil, the Church can’t anoint people with Shea butter. (I know. I feel your pain and I share it.)
Likewise, the Church can’t baptize people in hydrogen peroxide, even though hydrogen peroxide is, for some things, superior to water (particularly as a germ killer, and therefore as a symbol of cleansing from sin). The sacrament here, as elsewhere, symbolizes what it does and does what it symbolizes, and the attempt to “improve” it with different matter than that handed down from Jesus and the apostles results only in mischief. For hydrogen peroxide, while terrific at sterilizing, is not so good at communicating life. So water, which washes, drowns, and gives life is the matter for the sacrament of baptism which does all that to our spirits.
So here’s the thing: both marriage and ordination also have the matter they have because they are symbols that do what they symbolize and symbolize what they do. So the new Pope will not be embracing gay “marriage”, nor will he be embracing women’s ordination. Because marriage is the image of Christ the bridegroom and his bride the Church and the priest is an alter Christus, an image of the bridegroom as he stands before his his Bride in self-sacrifice. A woman can be a lot of things in the life of the Church, including hold offices of enormous power and influence such as queen, president, prime minister, abbess, hospital president, university chancellor, military commander of the French army kicking the English out, or any other office weilding power. So the notion that the Church denies that women are competent to weild power is rubbish. Likewise, women can and have held roles of great prophetic moment in the life of the Church, such as Hildegard of Bingen, Catherine of Siena, Teresa of Avila, or Therese or Lisieux. And of course, the single greatest member of the Church and the greatest creature in the universe is a woman: the Blessed Virgin Mary.
But for all that, women cannot be priests because Jesus and the apostles did not ordain women, not even the sinless woman Mary, as priests. Therefore, the new Pope–and all popes after him till That Day–will have no power to make women priests because women are not the matter for that sacrament. They are equal in dignity to men just as wine is equal in dignity to water. But wine is not the fitting matter for baptism any more than water is the fitting matter for the Eucharist. So no, neither this pope nor any pope to come will ordain a woman a priest.
On the other hand, not this Pope, I think, but some future Pope might decide to make a lay woman a cardinal, because cardinals are simply a human invention, cooked up in the High Middle Ages to help make a reasonably functioning machine for arriving at a new Pope. Just as your parish finance council is a machine built by human beings to get a bit of adminstrative work done, so the college of cardinals is a bureaucratic machine invented by humans which humans can change if they decide it prudent to do so.
I’m not saying some future pope will or should do this, merely that it is theoretically possible in a way that, say, changing the form of absolution to “Hey, don’t sweat it! Jesus sez it’s cool” is not possible. Learning what is reformable and irreformable in the Catholic tradition is not really all *that* hard, if the media would just make the effort. Unfortunately, it seems few do.
Meanwhile, let me just add this: Love that man!