One possible con of being raised totally without religion or spiritual tradition of any sort is that when you come to a point in your life where you are really seeking something beyond yourself, you may be naive and fall in with an extreme or cult-ish religion. I've seen this happen with a few of my friends who were raised with no religion. When they do "find God" as adults it tends to be in the extreme, and religion takes over their life, and it's the most fundamentalist and exlusionary type of religion.
Obviously this isn't a given, though - of the people I know who were raised without religion, most have just continued not to be religious and don't feel they missed anything.
I was raised within the Christian religion but not strictly, and had the unique experience of having a father who was really into theology (he now has his doctorate). He was always deconstructing religion for me and talking about it in "meta" ways. So my childhood was really more like a course in comparative religion than anything else, even though I went to a (liberal, progressive) Christian church and enjoyed singing in the choir and playing hand bells.
I also had plenty of exposure to fundamentalist Christianity in my extended family and it frankly scared me. The cons of being raised in a religion (any religion) where children are told that the way their family believes is the One, True Way is that frequently they grow up and come to a different conclusion and feel extremely bitter about the "lies" that were told them, and the warped worldview they feel their religion has given them.
Or, alternatively, they stay within the tradition. But, I will say among my many cousins who were all raised with the same type of fundamentalist, evangelical Christianity, only one I can think of has remained in the same church. Most have remained nominally Christian but have gone in really different directions (one cousin became Episcopalian, several just don't go to church at all and I don't know whether they still "believe".) One of my cousins is basically an atheist and has nothing but scorn for the tradition he was raised in. What I have noticed with people I know who were raised in "We Are Right, Everyone Else Is Wrong" religious traditions is that if they don't stay with it 100% (perhaps coming back after a brief period of youthful rebellion), they become apathetic and cynical in regards to religion, or go a completely different direction in their spiritual life.
Personally, we are raising our daughter with awareness of both the Greek Orthodox tradition (my dh's tradition) and the "liberal" mainline Protestant religion (my tradition). She is baptized Greek Orthodox. But, I will help her question, analyze, deconstruct and historically situate the traditions she is raised with, as developmentally appropriate, as she grows up. I definitely do not want to raise her in a "We Are Right" tradition. I think that is far more harmful than no tradition at all.