How will it happen? With a bang or a whimper? Will it completely die out? Or will it evolve into something completely different in terms of how it looks today. Obviously, there is a tremendous amount of upheaval surrounding this right now, considering the Church's activity in influencing politics and engaging in culture war. What say you?
To begin with, I'm going to assume that by Western Christendom you are also including Europe.
It's an interesting question. I would venture to guess that in some ways it will continue to evolve. The reality is that Christianity has been evolving since its inception. I won't go over that 2000 year history, but needless to say tracing the lines of thought makes it look very much like a family tree for different animal species. In small ways there will be changes and that will keep it from dying out or even really drying up. An acceptance of the sin of homosexual sex as an historical anachronism is one way that I see the religion evolving in much the same way that its opinion changed on slavery. I think we'll see more women in the clergy in protestant denominations and the Vatican allowing priests to marry in the upcoming years. I had a gay roommate in college and his boyfriend said that the seminary he attended was full of closeted gay men, but what can they expect when they condemn homosexuals to a life of celibacy and since priests have to be celibate anyway... well, lets say that those men see a confluence of life choices. That's why the end up with a cardinal having to resign because he had relationships with other priests. Also, the number of priests in the west is steadily declining. Part of that is generational, the current generation being less religious, but they might be able to pull in some more priests if they say that priests don't have to give up family life. My favorite priest when I was a child suddenly vanished. Years later, I found out that he had gotten involved with a women and got married. Those are some of the changes I think that will keep religion going in the west.
America is far different from Canada and Europe. In 20 years, I'd say religion will play an important part in the lives of 50-60% of Americans. It's quite literally bred into us here and won't be going anywhere anytime soon. I think there will be less religious people. Things that contribute are a diversity of thought, a diversity of people, a greater access to other forms of knowledge, and new social support systems, but America is special in its religious practices by having an open market. You can find a church anywhere to pretty much match your beliefs. It's a veritable buffet! Our younger generation is far more tolerant and accepting and that's part of the reason they aren't as religious. They see people protesting against birth-control pills and gay marriage and it turns them away. They don't want to be a part of it. That's why I think it'll change. In order to keep their numbers up, they'll have to. Those who don't, like the Catholic church, will dwindle more in numbers and importance and be left with a fervently devout core of followers who aren't going to go anywhere (child predator protecting be damned!) and have lots of little Catholic home-school children, like my step-brother and his wife. She's a baby machine and she's proud of it.
In all, I see religion in general declining in the west, but eventually hitting a statistical bottom where the number of converts and the number of deconverts will lead to stagnation. There are some people that are more keen to think supernaturally or whose life experience of hardship resonates with the Christian message and will be drawn to the claims of Christian belief. I doubt it will ever go away.