For the materialist, there is nothing beyond the physical world. Any supposed hint of a reality beyond matter is bogus, and the only way to discover laws about this world is empirically.
Thus, for the materialist, the word "truth" means only "that which I have personally discovered to this point, or which I accept from someone else's inquiries." Everything is relative, even intertial reference frames. Therefore, if two materialists disagree, the discussion would be about "your truth set doesn't intersect with my truth set, and you should change to my truth set." With two subjective truth sets at war, no objective standard is available. If one materialist is stronger than the other, he could force the other to pay lipservice to the other truth set, but even then the change is from one subjective truth set to another. Thus, the words "What right do you have to impose your morality on me?" is completely consistent with the materialist's presuppositions, and resulting worldview.
The Christian believes that there is something beyond himself, beyond humans, and beyond the physical world. Some hint of these things is available to every human and can be discovered (albeit imperfectly) through empiricism. But our chief source of certainty is God and His revelation. He peels back a corner of the curtain and reveals truth directly to us at times, through creation, Scripture, His Son, His Spirit, and all four working together.
Thus, for the Christian, the word "truth" does not mean "my truth." It means absolute, God-ordained truth. Thus, when one Christian says to another "What you've done is wrong," the first Christian is not saying "Your truth set does not intersect with my truth set." Instead, he's saying "There is an absolute standard of truth, including definitions of good and evil. And your actions are violating those standards." The issue is not, then, that one Christian is imposing his subjective set of truth on another Christian. It's that one Christian is calling another back to the objective truth that God ordained.
Physical strength ideally doesn't matter, and one Christian pulling another back from the precipice is not an act of arrogance ("My ideas are better than yours"), but mercy ("Come back to God's way! I'm not saying that my thoughts are better than yours, or that my truth is better than your truth! There is only one truth: the one created by the Way, the Truth, and the Life. I didn't invent it: I just recognized it when God showed it to me!"). Every person has some grasp of truth, but also has accepted falsehood. We can only assess our worldview's "goodness of fit" because there is a standard we are comparing our ideas and lives to: Christ. We know how close our lives are to the standard (R^2=0.999? 0.888? 0.222?) because a perfect line descended and made Himself known. To use another example from math, our lives are about approaching an asymptote ordained by God. What would our lives looked like if we no longer strove to approach the asymptote? And while we may not reach the asymptote in this lifetime, we can desire to reach it, and strive to reach it. In the process, the Spirit is preparing us for Heaven, where we will be made perfect. Don't you groan for that?