One thing that worked for me - as a parent, become more interested in it than they are. Obsess. Rather quickly, they will discover it is “uncool” and move on. Alas, what they move on to may be worse. And you may never get “it” out of your system. It did work for at our house for Pokemon (on its first go round).
Oh. I’ve heard of that, of course, but I didn’t know anything about it, or that it contains modern music. I just assumed we were talking about something other than the play. 
My younger brother once had to be told that, while playing the record you’ve just bought [a lot] is to be expected, playing it [six times in a row] is not to be accepted. A limit of twice in a row for new purchases was set thenceforth, after a short negotiation involving both the offender and those multiple parties whose ears were starting to get thoroughly offended.
If it had been the other brother, starting with an initial tense “do you realize it’s the sixth time in a row you’ve played that record?” would have caused a teenaged explosion involving angsty accusations of abusive mistreatment, from which things would have gone downhill. The fallback could have lasted for months… Middlebro is one of those people who nurse their offenses more lovingly than their relatives. The tack to take would have needed to be very different.
So, another one for “only if it’s starting to be damaging to themselves (including damaging the nerves of the people with whom they share housing)” and “the exact way to do it would depend on the individual”.
My daughter went through a period of being obsessed with her old yearbooks. It was kind of bizarre and I must say I still really don’t know what that was all about, but it got better. She also worked on the yearbook committee in high school, so I guess that turned out well.
She also went through the Harry Potter phase at the same time everyone else was going through it. Now she is a Disney-obsessed adult. Pretty sure I just got a weird kid!
She’s way better than me, y’all would like her.
For those whose kids played Hamilton (or whatever) incessantly, maybe the solution would just be to compel them to play the music with headphones only, but not limit the number of times to be played?
I’ve been in more than one subway train in which I could hear clearly the music others were playing with headphones on. At those volumes, it’s still bothersome as well as being unhealthy for the person with the headphones.
It all passes. And why would you take something they love away? Unless it’s affecting quiet enjoyment of others, or hampering school etc.
Well, this.
Hell, I’m over 50 and I still tend to obsess over stuff (band, books, movies, food, whatever). I’ve found that when I do it, it’s because I’m seeing something interesting but unexpected in the whateveritis and I want to get a better understanding of what it was that grabbed my attention. To get there requires a certain, noticeable immersion for a while. The “obsession” passes eventually, but I keep that better understanding of whateveritwas. I think that’s called “growth”.
… you realize you do have a really big target on your back when it comes to “obsessions”, right Inigo? 
Thinking back to any teenage obsessions I had, they all passed by my first couple years of college so I’d expect the same from my kids. Chances are, they aren’t going to run away from home to tour with a band or anything so, provided they’re not blasting music throughout the house or shoplifting t-shirts, just ride it out.
Maybe we are comparing different things.
I can understand that playing the same piece of music in the house loudly is rude to others. (As has been said, use headphones.)
But what about obsessions that lead to a career?
I practised / played chess ‘obsessively’ from the age of 6 onwards.
I became internationally rated and travelled all over the world for tournaments.
I made friendships that have lasted 50 years.
Whilst being a computer programmer, I earnt extra money from chess (teaching and writing.)
Eventually I got a marvellous full-time job teaching and organising chess.
Touche’
And you know what, even if they did that’d be kinda cool.
I think as long as it’s something that’s not impeding my children in some way, or causing discomfort/annoyance to others, I’ll probably indulge their interest.
But if they’re wanting to do stupid stuff like skip their first year of college to follow a band around the country, or being so wound up in something that they neglect their studies and/or hygiene, or it starts to affect being relatively normal (i.e. some kind of weirdo shut-in who is obsessed with Star Trek or something), then the hammer’s going to come down.
Everyone gets obsessed with something as a kid/teenager, to a greater or lesser degree. I was absolutely enamored of being a football player and athlete. And my parents were cool with it, so long as I kept my grades up. It ended up taking a couple of knee injuries and subsequent surgeries to break me of that obsession. I knew other guys who were consumed with bands, or other activities or sports. I mean, one guy I knew was a Depeche Mode superfan- to the point of scrounging up concert tapes of performances in Japan. In 1989, prior to the Web. He turned out fine for what that’s worth.
The only thing about my daughter’s music that bothers me (other than that it’s a style I really don’t like) is that she listens it on her iPhone speaker.
I give her one snarl of “tinny speakers…Grrrrrrr…” and then tell her to shut it off. She understands that if she plays it on a Bluetooth speaker I don’t mind at all. The problem is that for her to enjoy the music she needs to jack up the phone volume so much that the highs punch right through our walls to the far reaches of the house.
I don’t understand why she can’t use headphones or a Bluetooth speaker–I accept the music as long as it’s not shrill and tinny.
With regards to the OP, I have a concern if the obsession takes over one’s life. I have one kid who is so obsessed with gaming that I can’t see how he will ever get serious about a job, and he’s already in his mid twenties.
For an adult kid there is little to be done, of course. I guess the question is how you moderate behaviors in minors that aren’t bad in themselves but could get bad in excess. I watched a lot of TV as a kid, but I don’t any more. My daughter watches a lot of dumb YouTube stuff–should I be concerned? Probably not, but you don’t really know.
I probably should add a clarification to my example … they weren’t *playing *Hamilton all the time, they were singing it! So, yeah, headphones not helpful.
Generally speaking I approve of singing, as a nice cooperative communal activity that promotes group bonding (and I’ve gritted my teeth through a number of TRULY AWFUL renditions of Bohemian Rhapsody from all three of 'em together in service of this belief) but of course it’s not very bonding if only two of the group are pro- and one is violently anti-
I’m just an uncle, but I relentlessly pick at my 15-year-old niece’s main obsessions, which have been Thor and Ninjago for at least a half a decade now. (She’s a tomboy, obviously.) At first I was just trying to get her to realize that other good things existed besides her main obsessions, but at this point I’m mostly just doing it to screw with her.
This sounds like the way some Metallica fans acted in the early 1990s and KISS fans in the late 1970s.
As long as it isn’t interfering with a child’s schoolwork or peer relationships, and they’re able to talk about other things (and not bring it up at inappropriate times, especially when they’ve been talked to about it) and they aren’t stealing to buy memorabilia or lying about their whereabouts if the celebrity is in the region, it’s yet another “pick your battles” thing.
I’ll never forget when I had to do an ancient Rome-themed poster for my history class, and made one advertising a concert by the “Pompeii City Rollers” and incurred the wrath of a couple of my friends, who thought I was insulting the Bay City Rollers. :rolleyes:
My Little Pianola was obsessed by Wittgenstein’s Tractatus Logico-Philosophicus as a small girl, until I whapped her in the head about eleven or twelve times.
Very sensibly, too. What if she’d been seduced into reading Heidegger?