Agree or disagree with monarchists, but I think you need to re-check your view of this "democratic" nation against the reality of the situation.
The nation you define as a "robustly Christian nation, (the most Christian in the world)" has long since left the Christian concept and adopted neo-paganism. Your "Christian nation" upholds the people's "right" to pornography, and spreads it to the 4 corners of the world (Playboy was one of the first things tossed on the Iraqi people after we "liberated" them), and refuses people the right to pray in schools, or display religious symbols on public grounds. It is one of the world leaders in the murder of babies still in the womb as well as contraception, and not simply in promoting these ideas the world over, but using federal funds (that's OUR money) to do so. This "most Christian nation in the world" is also one of 3 (I believe) in the world to now have legalized sodomite "marriages".
Yes, you are allowed to embrace the Catholic faith, but not too loudly, lest you offend someone else who is exercising their right to embrace Islam, Satanism, Sodomy, or any number of other things the Catholic faith denounces.
I think the comparison to what your rights would be in the kingdom of Saudi Arabia is somewhat irrelevent, though. As we are seeing in Iraq, your rights to practice Catholicism would be no better there if you were talking about a democracy in Saudi Arabia. In fact, we have recently seen that many Christians are fleeing Iraq now that a democracy is being established because the majority vote will now go to a group of muslims that are more extreme than Saddam Hussein, who allowed Christianity.
This is the major problem with democracy, it's laws are determined by the majority rule, not by an objective view of right or wrong- might makes right in a democracy. So, when the majority of people get holed into believing that it is ok to kill babies (or are at least brow beaten to the point where they won't stand up and fight it), suddenly baby murder is OK, sodomites are O.K., indeed anything is o.k. The only thing not tolerated is people who are "intolerant"- that being Catholics.
The reason the writer is so supportive of the monarchist form of government is that it mirrors the form of government that Christ established in His Church. Authority comes from the top down. Ideally, the monarch would be held in check by the Papacy, who is responsible before God for every soul in the World, and so ensures that the temporal rule of law does not contradict the Divine Law. In temporal matters the monarch is like a father to his nation, and is likewise responsible before God for his people.
The democracy is the inverse of this. It displays the anti-christian idea of authority coming from the bottom up. Each individual is himself the source of authority- echoing satan's "I will not serve." or satanist Anton Levy's verse "Do what thou wilt".
Plus, since the politician has as his goal to get elected, he is going to do what it takes to accomplish that, even if it is not in the best interest of the people. If a monarch is to leave the kingdom to his heir (presumably his child), he is going to be more likely to do what is best for the kingdom, so his heir doesn't simply inherit a bankrupt mess.
Clearly this does not mean we are doing something wrong by participating in the democratic process- provided we are voting for people who aren't opposed to God's laws. Right now that is all we can do.
One doesn't have to look around very long to see that this shining star of a republic is running down hill pretty quick, and drowning in the mire of it's own corruption. What happens next is simply a matter of history repeating itself, and it involves a head to head collision with Divine Justice. When a people continue to cry out for their liberty to practice self governance and the uninhibited pursuit of self gratification, God more often than not doesn't send a flood of water. He simply lets the people have their way, and they drown themselves in their own "liberty" and the filth of their inordinate desires.
Even leftist Steven Spielburg was able to point out that when given the right to choose their own leaders, man has most often ended up empowering a tyrranical dictator. You could consider that the power hungry court system now, or some as yet unknown event to take place not too far in the future- but a society which tosses off the authority of God will always fall under His judgement. In a democratic society, the whole of the populous bears the responsibility for that, not simply a king who is lording over God's people unjustly.
I think your selling America a little short on the religious thing. After all, we swear "So help me God," we light the National Christmas Tree, and attend church services with far more frequency than any other people. Really, I think this is the most Christian country in the world. I can't think of any other, can you?
All of this is not to say that democracy can not go horribly wrong. In Germany, Schroeder deliberately left "God" out of his oath of office. In England, Catholics STILL aren't allowed to be Prime Ministers. The Dutch regularly kill off Grandma. We can wear our crucifixes to work and school; but in France there's a law against it.
But America is definitely different. The PEOPLE of the United States are among the most resistant to abortion, gay marriage, etc. all the things you mention. The Justices of the Supereme Court, ( forget the presidency: these people are the closest people we have to monarchs in this country,) are responsible for our current situation. The people are not crying out for more liberty, or lisence, to destroy themselves. It is being forced upon them by a minority population of special interest groups and an unelected judiciary. This is a result of imperfect democracy. WE need more democracy, not less.
As far as the whole issue is concerned, I am not arguing that monarchy is necessarily a bad form of government, or that democracy is appropriate in all situations. I simply must insist that democracy can not be branded as anti-christian. I might go so far as to quote mr. scary evangelical himself, Attorney General Ashcroft: "We have no King but Jesus."