"No great advance has ever been made in science, politics, or religion, without controversy."
One limiting factor in knowing a religion is false is the tendency of religions to form around clusters of doctrinal points, rather than a single point of doctrine. Unless you are some sort of past-master theologian, I doubt you can systematically undermine each and every point of the target's entire religious belief system. Other limiting factors: the antiquity of some (if not all) the events described by doctrine, and the selective nature of revelation and calling.
With this in mind, I think the responsibility to spread the truth (some say "the Word" or "the Good News") is as important as the the right to be wrong. Maybe folks don't like the facts, but a God worth the worship values truth over falsehood. It's OK if you don't feel a calling to evangelize; but if your target's misinformed beliefs distance him from God, you do no service to God, self, or other by keeping silent.
Being wrong does not make people happier, just more maladjusted. It is not happy-making to live a lie. If you believe you should do unto others as you would have done to you... well, wouldn't you prefer to be properly informed?
I think it not inappropriate to use this space to plug two of my favorite books on the topic: Truth in Religion and How To Think About God.