If one want to address the rise or decline of religiousity, one must look at living standards. Early on one commentor reminded the thread about how religion is ever so present in poor nations yet there is a clear lacking or at least a clear separation of religion to everything else in life for generally rich people (unless you are American where you decide that you will be rich and religious, much to the contradicting standards that it shows

)
So lets say by 2200 the lasting peace we have stays and manages to get us:
a)remove all known existential threats to our society (say Global Warming, mass consumerism threatening our access to resources, etc)
b)remove all known social impediments to our society (say media bias, privatization of all the world to the suffering of those affected [getting images of Shell in Africa ruining local culture to mine oil], active and shady connections to corporations that could be viewed as a global oligarchy of industry, etc)
c)Thanks to the previous two a reasonable middle class of the whole world with a respectable upper class. Essentially, our currently hoped utopia
If life is fine around the world and the known social and existential problems in our society nearly eliminated, everyone should have a good living condition and like most current 1st world countries, gradually become more connected to logical thinking and knowledge around the world (and thus less dependent on local thinking and knowledge [I finally don't have to hear from my dad that I will get the cold because "the cold-ness seeps into your skin and weakens you bones"] so you won't get stuff like, say, acid attacks) and subsequently the necessary settings that religiousity needs to thrive are suddenly gone and with them, religiousity itself gradually sinks.
This doesn't mean that people are all suddenly Richard Dawkins-style atheists, it just means that you are less likely to hear "Allahuackbar" really loudly in a crowd or hear a bunch of mormon people selling religion or hear the occasional senator who wants the ten commandments as law.