My hypothesis

[GUBU]

The problem with your theory is that the "information age" has not given any info about the nonexistence of God. So, religion will thrive until it does. And if extinction is in the cards, it won't be because of Christians. It will be in spite of them.

The problem with your conjecture is assuming that religion is thriving, when it is not. In most countries religion is dying, albeit slowly in most. But the fact that apostasy is very high even in religions where the penalties for doing so is high (for example in the UK the highest growth community for atheism is amongst second and third generation immigrants from muslim majority countries), and the fact that most of Europe is either officially majority arreligious (like the UK, France or Czech Republic), or functionally majority arreligious (like Ireland or the Netherlands) and many other countries not far behind (for example in the US the fastest growing religious position is atheist/agnostic encompassing c.20% of the population) shows this to be a fact clear as day.

In fact it is only in theocratic dictatorships or other countries which enforce death penalties do we see religion clinging on, and oftentimes the arreligious in those countries are keeping their heads down and mouthing the appropriate policies out of fear of losing their heads.