I haven't played MCC, but if 343's previous games are any indication this post may be helpful.

343 mixes their stuff 'correctly' in that the dialogue is only on the center channel. Bungie always has dialogue on Center, Left, and Right.

If you have your Xbox set to output 5.1 or 7.1 and you only have stereo speakers, all the other sounds can overwhelm the center channel. If you hook up to an amp, see if you can boost the center channel. Otherwise, set your xbox to output stereo.

If you are listening on a 5.1 system, turn up the center speaker.

That would be my guess.