Of course, much depends on what is meant by “anti-Western”. If it means chucking the baby of 2000 years of Christian theology and culture along with the bathwater of brainless, hedonistic, consumer, godless, post-Christian consumer culture of death idiocy, then it will fail as the latest and dumbest form of post-Christian Protestantism.
But it need not do that. It could remain grafted into the vine of the Catholic Church and attain great heights in a renewal of the Church that will stun and amaze the West as it goes down under its hubristic doom. Particularly if the West decided to harden into the anti-Catholic culture as it seems to be toying with.
There was a householder who planted a vineyard, and set a hedge around it, and dug a wine press in it, and built a tower, and let it out to tenants, and went into another country.When the season of fruit drew near, he sent his servants to the tenants, to get his fruit; and the tenants took his servants and beat one, killed another, and stoned another. Again he sent other servants, more than the first; and they did the same to them. Afterward he sent his son to them, saying, ‘They will respect my son.’ But when the tenants saw the son, they said to themselves, ‘This is the heir; come, let us kill him and have his inheritance.’ And they took him and cast him out of the vineyard, and killed him. When therefore the owner of the vineyard comes, what will he do to those tenants?” They said to him, “He will put those wretches to a miserable death, and let out the vineyard to other tenants who will give him the fruits in their seasons.” Jesus said to them, “Have you never read in the scriptures: ‘The very stone which the builders rejected has become the head of the corner; this was the Lord’s doing, and it is marvelous in our eyes? Therefore I tell you, the kingdom of God will be taken away from you and given to a nation producing the fruits of it. (Matthew 21:33-43)
What is striking when you read the New Testament when it addresses the persecution visited on the Church is how little whining there is about how unfair it all is, or how the Church is on the ropes and doomed. Rather, the note sounded, as above, is how doomed is any opposition the Church faces. It’s a remarkable attitude for a vanishingly small sect in a sea of hostility to take. It should still be ours. The problem is, as is the custom of our time, we politicize everything and so we assume that if the Church is not succeeding politically or with the manufacturers of culture in the commanding heights of demonically-occupied DC, NY, or LA, then we are nowheresville. That would be like Paul calling his mission a failure as he was being frog-marched out to the axe. He wasn’t so limited in his vision. We shouldn’t be either.
The question is not whether the Church will survive the West’s growing rejection of Christ. It is whether the West will. Only one seventh of the world is Christian. Much of the world has never had a crack at the gospel at all. We’re not even close to finished, I reckon.