TL;DR: Gertrude for iOS (iPhone and iPad) can now block all album artwork, images, music videos, and embedded Apple TV content from within the Apple Music app, allowing kids to listen to music without being exposed to inappropriate imagery.

Gertrude is a free app that can block content selectively, even inside other apps. I'm a computer programmer and dad, and I built the app originally to fix a loophole in Screen Time introduced in iOS 17—Apple removed the ability for parents to block the GIF search #images feature in the built-in texting app, exposing millions of kids to inappropriate content. Gertrude started by blocking those GIFs and has grown to support 10 different types of blocking.
In the 2 years since it was released, we've added support for blocking:
I also built the app to allow me to immediately roll out new blocking rules when Apple made updates, or in response to user requests. So when two users reached out within a few weeks asking if I could block images and videos in Apple Music, I was able to create a new block group.
If you haven't installed Gertrude yet, just download it from the App Store and run through the setup. You'll be able to choose which block groups to enable during onboarding, including the new Apple Music one—all groups are enabled by default.
If you already have Gertrude installed, it's a little more involved. Because we don't want to silently change behavior for families that are already relying on the app, new block groups are opt-in for existing users—the Apple Music group won't turn on automatically when you update.
If you have a connected Gertrude account (it's free—more on that below), you can enable the Apple Music block group directly from the parents' website without touching the app at all:

If you don't have a connected account, the quickest path is to delete the app and reinstall it. That sounds more drastic than it is—there's no stored data to lose. You'll just run through the two-minute setup again and choose Apple Music blocking when it appears in the list. While you're at it, I'd encourage you to connect a free Gertrude account during setup. It takes about a minute and means you'll be able to enable new block groups like this one from the website going forward, without having to reinstall. (I really need to write a dedicated post about the free connected account feature—it unlocks a lot. I'll do that soon.)
This feature came directly from two different parents reaching out asking for it. I'm genuinely interested in hearing what other things you'd like to block on your kid's device—if you've found a gap that Gertrude doesn't cover, send me a message. No promises, but I read everything and I've shipped several features because a single person asked.
The Gertrude mac app helps you protect your kids online with strict internet filtering that you can manage from your own computer or phone, plus remote monitoring of screenshots and keylogging. $10/mo, with a 21 day free trial.