A couple of points.
1: this debate matters. I find it uninteresting, full of logical fallacies, and ignorance. However, when people who 'believe' this are members of government, and are basing their political ideas on this, then yes, it does matter.
2: Whether you ask me to 'respect someone's opinion', or 'respect someone's belief', it results in the same. Anyone can claim something, use a metaphysical argument to show that I cannot, strictly speaking, prove him wrong, and get away with it.
3: Please read this entire discussion, search-and-replace "GOD" with "flying spaghetti monster", and see which side you're on now.
4: Reasoning according to the Situation's beautiful paragraph about why YEC believe what they believe (which is actually quite clear and well-written), one might also establish that the Earth is 5 days old. No one can disprove that. If God is all-powerful, surely he can manufacture memories? In fact, according to that reason, God could have done literally anything, covered it up, and we wouldn't know. Meaning that, again, anyone could claim anything and get away with it.
The true acid test of Christianity lies in the only source that truly and completely supports it: the Bible. If the Bible is the word of God, then yes, Christianity is true. If the Bible is a historically accurate description of events (most importantly the part about resurrection and stuff), Christianity is a valid belief. If, however, the Bible is a book written by men, with paticular socio-political objectives in mind (reforming Judean society), then Christianity becomes shaky at best.
That is not to say that Christian morals are wrong. One can have perfectly good morals without resorting to religion. In fact, take the ten commandments, take out the ones about God, and you've got a set of moral rules that isn't entirely unreasonable. I personally would adhere to different ones, and that's the debate we should be having.