This dogma has always been a hard teaching for me. While I don't subscribe to the strict interpretation advocated by Fr. Thomas Feeney et al, I have to accept this dogma as I accept all other dogma of the faith. Here's how it is presented in Lumen Gentium 14:
Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and Baptism, and thereby affirmed at the same time the necessity of the Church which men enter through Baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.
Where I tend to get caught up is in the question of invulnerable ignorance. As I mentioned to Simon-Peter, though, culpabilty is not something we have the ability to assess. God doesn't determine someone's culpability on the same grounds as your average civil court. He sees all of the mitigating factors of which we are clueless. However, we don't have the luxury of omniscience. We have to operate on objective conditions. And if we believe someone is mistaken, invincibly ignorant or not, we have to attempt to bring them back. I believe the dogma EENS speaks more to our obligation to evangelize than to the fate of others who deny the truth of our faith.
So this brings me to the question of truth and what we owe to it.
As Catholics, we can take some guidance from the different levels of Magisterial teaching. Donum Veritatis 23 explains three levels of Magisterial teaching, two of which are pertinent to this discussion in that they fall into what we as Catholics are to accept as infallible teaching:
When the Magisterium of the Church makes an infallible pronouncement and solemnly declares that a teaching is found in Revelation, the assent called for is that of theological faith. This kind of adherence is to be given even to the teaching of the ordinary and universal Magisterium when it proposes for belief a teaching of faith as divinely revealed.
When the Magisterium proposes "in a definitive way" truths concerning faith and morals, which, even if not divinely revealed, are nevertheless strictly and intimately connected with Revelation, these must be firmly accepted and held.(22)
When the Magisterium, not intending to act "definitively", teaches a doctrine to aid a better understanding of Revelation and make explicit its contents, or to recall how some teaching is in conformity with the truths of faith, or finally to guard against ideas that are incompatible with these truths, the response called for is that of the religious submission of will and intellect.(23) This kind of response cannot be simply exterior or disciplinary but must be understood within the logic of faith and under the impulse of obedience to the faith.
Different levels of Magisterial teaching command different levels of adherence, as I mentioned in a previous post. Those teachings that are not infallible but are related to faith and morals require "religious submission of will and intellect." This is not the kind of commitment one expects of Truth but of facts. We might not understand all of what is being taught; we might not agree with it for various reasons; but we are willing to submit out of trust to our Holy Mother Church because She is the authority, and we trust Her.
But what, then, of the other two degrees of Magisterial teaching? Those things that are not divinely revealed must still be accept with firm assent. Those things that are divinely revealed (dogma) must be accepted with theological or "divine and Catholic faith": that is, without reserve, we must commit ourselves to these matters as Truth whether it matches our preferences—whether we like it or not.
When we read such words, it's easy for some of us to balk, to say "that's not what I signed on for." I didn't agree to set my brain on a shelf. I ddn't agree to give up free agency.
When we think along these lines, we're forgetting a very important detail. Above all, we should be seeking the Truth. A life that pursues anything other than the Truth is not worth living. No one wants to live in utter self-deception, although many people try. To live for anything but the Truth is to waste our lives.
That's a simple enough concept that enough of us get it wrong. It's deceptively simple. What's more basic is that most of us don't understand what the Truth is, or more correctly who the Truth is. The Truth is not a something but somebody. To deny the Truth is not to deny mere facts but to deny the One who is and was and always will be.
Jesus Christ is the fullness of revelation, the verbum abbreviatum or abbreviated Word of God. The dogmas of our faith are revealed truth, so in some way or another, they express some aspect of Christ Himself, not just a fact about something He said or a detail about what the apostles ate for breakfast one day. To reject dogma is to reject Christ. If we understand nothing else about our faith, we must accept this.
UPDATE: Doh! I nearly forgot to point to this post by Marcus Magnus at Dominican Idaho on Rejecting Error.