You posted: If we truly believe in Christianity, we ought to challenge others’ beliefs, showing where we disagree.
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I think it is easier to challenge the beliefs of those who actually hold beliefs closer to our own, because we come from the same frame of reference. When we challenge the faith beliefs of those whose faith is SO different from our own it seems to me it becomes much more difficult. For example, you just cannot effectively argue Scripture with an atheist, or a Buddhist, for that matter. Mormonism seems to come closer to my Christian beliefs (I am a Methodist, but I don’t even agree with all of the positions that they hold.), so perhaps that is what creates the tension. But Mormons have additional writings in which they believe and in which I do not. How do you tell someone that their faith is wrong? I can tell people why I believe what I believe, but ultimately they have to make that decision.
Easy...
First; you must actually KNOW just where/who/what their faith is placed.
Second; then you can show where the object of their faith is non-Biblical.
Third; the Holy Spirit does His part of the bargain.
I try to keep opinion and 'tradition' out of the mix; for they are quite subjective.
Logic works on raw data; emotion works on experiences.
You'll have to define 'they' and also 'positions'.
I attend a WESLEYAN congregation myself.