Although I've always liked to believe that some movies are made without music so that those of us who have auditory disabilities aren't excluded from the audience, after researching a bit I think it's a slightly different reason. Often the music in movies is so loud that even non-disabled people have trouble hearing what the actors are saying. When you do a Google search about music in movies, the most numerous results are pages where people are asking why movie music is so loud that they can't hear the dialogue. Even reading YouTube comments on any random video, you'll see a majority of comments saying that they couldn't hear the actor/narrator because of the too-loud music. It might be more likely, then, that some movie makers acknowledge the ridiculousness of covering up the vital parts of the movie, like the dialogue, with "mood" sounds and that they omit or limit music for that reason. Think about it: if the story is immersive enough, if the actors are engaging enough, if the director is good enough, etc., then excessive music wouldn't be needed to add artificial "mood." Heck, of the available movies have had no music at all, the lack of music went entirely unnoticed by most viewers. That proves that music is often unnecessary. :)
Besides being unnecessary, music is often intrusive. In our society, we're surrounded 24/7 by music, no way to avoid it entirely. Can't go grocery shopping without getting our ears blasted. Even kids in school now are bombarded with loud "study help" music in the background, and at my niece's day care they turn on "nap music" cranked to 11 while the kids toss and turn and try their best to stay still and pretend to sleep during the two-hour noise blast. The absence of music in a movie gives people a break from the constant noise and lets people focus on the movie, really getting immersed in the movie without the distraction of the music attack that we have to struggle with in daily life.
With just a bit of research and reflection, I can see that there are more reasons for a movie to have no music than to have it.
Personally, I have hyperacusis and can't stand to hear music. Hearing music, even low-volume music, breaks down muscle tissue throughout my body, feels like my all of my muscles head to toe are being ripped out. This problem drastically limits the number of movies I can watch unless I mute them and only read the subtitles/captions. I wish the home releases of movies (DVDs, digital, etc) had an option to omit the music for the inclusion of people who have hearing disorders. I remember watching the movie Lion and saying to my friend, "this is awesome -- there's been no music since the movie started!" and right about then the first song started. Sigh.
(By the way, I'm new to this site and this is my first comment. I hope I'm doing it right. There's a huge intimidating list of rules and I hope I'm following them correctly so I can get some practice participating in meaningful discussions since my disability prevents me from participating in most in-person interactions. :) )