In my church (and what I hear from colleagues who attend other church's in the same city) the youth, are sadly quite theologically ignorant. I am a youth myself (19), and I quit going to Friday night youth meetings long ago because it was just such a waste of time. Trying to keep the youth on the right path in Christ - keeping them away from drugs, sex, alcohol, and all the evils of society seems to be the main focus - theology is just a non-issue. I certainly dont consider myself sufficiently educated yet, but the point is, all that I do know has come about as the result of my own personal study instigated by my own personal thirst for knowledge; rather than being motivated or influenced by the church itself. My church seems to care less whether the youth actually understand the Incarnation of God and the redemption of mankind, as long as they attend liturgy every week to celebrate these events, and live a moral life to enjoy the fruits of these events.
I have had the desire and personal motivation to make theology a hobby, such that I would go out of my way to read and learn for myself. Most of my friends, and the youth in general, simply dont have this mindset at all - they're good Christians, better than myself, and they're very concerned about their spirituality, but their concern for theology simply doesn't exist. Seeing as todays youth are tommorows leaders of the church, I believe my church is making a huge mistake by being negligent with regards to educating the youth on theological issues.
Furthermore, the fact we live in an age of ever-increasing skepticism means that the church really needs to put its foot down. I had one friend who nearly converted to Islam due to his ignorance - the church blamed his parents for not keeping an eye out on him - I blame the church for not sufficiently educating him to realise he was being duped by islamic lies. Skepticism and polemical attacks against Christianity from all sorts of perspectives (atheistic, islamic, Jewish etc etc) are everywhere - on the internet, on the radio, T.V., at work, at school, at social functions - ignorance today is a dangerous thing for any Christian, especially vulnerable youth.
The Lord promised he would not let the gates of hell prevail over His church, so I find hope in this promise and allow that hope to dissolve my fears that the youth's ignorance will be the church's downfall (in my region at least)....