I think that during the twenty-first century several forces will either change the Catholic Church beyond recognition or completely obliterate it.
The first I think is demography: even though Christianity began in the Middle East and the Mediterranean, it later spread to Europe and from Europe to all the other continents. But, today the homeland of the Catholic Church -- Europe -- is less Catholic and Christian than ever. In fact, the biggest concentrations of Catholics in the world are outside Europe in some of the former Catholic powers like Spain and Portugal. How will Catholicism look like when most believers (and necessarily an increasing number of the higher-ups in the clergy) will be from America and Africa, and maybe Asia. Not only fewer and fewer Europeans and North Americans are believers, but even those believers are in risk of being outnumbered due to low birthrates. Now, I don't think that Catholicism is the same everywhere. For example, think of the great admiration in which John Newman is held by English-speaking Catholics, but he is virtually unknown to Spanish-speaking Catholics. Catholicism will change, therefore, in this century solely for that reason.
The second I think is, of course, other religions that will compete with Catholicism. The first battle that Catholicism lost was the battle against Protestantism (or mayby, the battle against Eastern Orthodoxy), which divided European Christianity. But Christianity was never able to attract Muslims in the Middle East and elsewhere, who have been visited by European missonaries for many years now, and have been in touch with Western culture even in the days when Christianity was a big part of it. Or, think of the failure of Catholicism to take root in East Asia. In both these places there are rich religious traditions that Catholicism is not able to replace.
The third is, the possibility of scientific progress in the twenty-first century. Looking back to the discoveries of the nineteenth and twentieth centuries, one can only imagine what this century will bring. So, not only Catholicism may be undermined by other religions, but all religion may be undermined by discoveries that give naturalistic and godless answers to important questions. Religion can of course try to adapt to a naturalistic point of view, but there is only so much naturalism that religion can accept.
Finally, I think the weight of the criminal failures of the Catholic clergy will tend to discredit them. How can an institution -- indeed, how can a single man like the Pope -- claim to be infallible in matters of morality when not only their clergy abuse children, but cover it up as much as they can? When you claim such moral knowledge you must be held to a higher standard. But, maybe now in the twenty-first century people will no longer look the other way at the moral failures of the Catholic priests.
What do you think? Will the Catholic Church survive the twenty-first century? Whatever happens, would that be a good thing or a bad thing?