Aspie (I prefer HFA) mum of a much younger suspected HFA boy here and I think I get some of your concerns. I was easily led/pulled into strong obsessions at your son's age so I suppose an issue to consider might be how healthy his peer group's views of women (or people generally) are - whether the music (I haven't listened) could be symptomatic of something that could become a wider problem, if that makes any sense. As I am sure you know (but others on the thread may not) even high functioning individuals on the spectrum can have real struggles with peer relationships and be vulnerable to bullying and exploitation. It is also easy to fall in with people who aren't the best just because they act like they accept us. We can also take things literally when they may just be dramatic posturing for others.
In terms of the meltdowns I would wonder about how important identifying with this music (or using it as a means to be accepted in a particular peer group) is for your son. But (from painful experience) he could equally be vulnerable in a group built around politics, religion, programming, gaming or whatever else if the group itself was an unhealthy one, if that makes sense?
Alternatively of course it could be a special interest. From my own experience it feels pretty tortuous to be unable to indulge in my own special interests - it is like sleeping or eating (which I will happily forgo for extended periods without even noticing, in favour of the interests!) In my 40s, I am far more able to self regulate than in my teens, but when I was unable to pursue an interest due to the location in question permanently closing, I experienced strong grief, like a death. I cried for days. I don't do involuntary change about (what I feel as) important stuff easily, even when it's no big deal to others. And that tends to be part of the aspie profile.
I don't know how ADHD complicates things but I wonder how your son would react to you as non judgementally as possible asking him what the music means to him and whether it is more about relaxing, belonging or something else? It might not work, but it could help you to help him understand situations he might find himself in, again if that makes sense? That connection may be more important than this particular battle in the long run. Once he grows up and moves out he will likely still need support to understand the world he finds himself in. Do you have any external support around his diagnosis? (Some charities provide peer support).
I'm not looking forward to being in your position - I am sure it will come, with music or something else. If it is any consolation, when I went away to uni and made a new group of friends my interests changed a lot when my routine changed. I also worry about my son attracting some of the painful experiences I have had - but at the same time, I know I lived through them. It's amazing the amount of resilience you pretty much have to develop by the age of 17 as an aspie just to survive to that point in school. (Possibly also worth mentioning that my special interests are a lot like a release valve for stress - they let me block it out for a while. If that is what is going on with your son, lockdown might be an especially difficult time to be without his music. For me, obsessing about special interests can be one of my first indicators that I am under a lot of stress, even if there are no other obvious signs. I don't emote in a typical way.)
Oh, and again I am no expert on ADHD, but at 17 I thought I needed music to study. A few postgrads later I know that for me anything but utter silence is a massive distraction because I tune to the aural input over what I am reading and the change in songs interrupts my concentration. Your son's profile may be the opposite of course, but at 20 I completely convinced myself I needed to do my special interest to focus while studying. What was actually happening was that I found studying stressful, needed to build in time for the special interest as a release, but felt I had to optimise the study time (all or nothing) so did both simultaneously and very much non optimally. That may not be what is happening, but it's not impossible. Are there other ways your son could be helped to recognise/mitigate his stress levels if that is what is leading to the obsessive behaviour?
Sorry this is so long - I hope some of it is helpful, though. Good luck!