Are religious people supposed to go around "debunking" other peoples belief just because we believe differently than they do?
Yes, that is what the bible demands (proselytize).
But, don't worry, they only debunk Pagan, heathen, and Satanic beliefs (like Christianity, Judaism, Islam, and all of the other religions on the planet) (I'm kidding, of course). The problem is, everyone believes that their religion is correct, and that automatically makes all others wrong.
When Jesus said "judge not, lest ye be judged" (Sermon on the Mount), I think that he was letting us know that we should be tolerant of other religions.
Yet, we should not follow Satan, and if we don't judge who Satan is, and don't judge what Satan does, we will end up following him. We have to judge to discern right from wrong.
So, we must judge, but we must not be judgemental to others who merely seek to follow their own religion.
It seems obvious, to me, that God wanted us to build bridges of understanding with other cultures, other religions, and people of other languages. This is why he scattered the races, changed their languages, and did all this at the Tower of Babel. We are supposed to accept others, learn their versions of God, and merge with them to gain an even deeper understanding of our own religion.
After all, if all are God's children, then all must have had some version of God's word, and we would have to study that in order to understand all that God meant to tell us.