A typical linguistic eggcorn, the moot point is occasionally mispronounced as a moot point. Moot and mute may appear to be identical terms at first look, but they have different pronunciations and meanings.
While moot rhymes with boot, mute rhymes with cute. The words moot mean something irrelevant and mute means silent.
It's understandable why some individuals could conflate the two terms in this phrase. It would be reasonable if someone said something was a mute point even though the assumed meaning—"the point is silent"—still makes sense. It's important to understand that the right expression is a moot point rather than a mute point.
When used as an adjective, moot designates something that is up for debate or has no bearing on practical matters. Mute as an adjective denotes silence or lack of speech.