Whether you can find satisfactory alternatives depends on what your end goals are.
I use neither Apple Music nor Apple Photos. My alternatives are tailored to meet my needs, but they are also more expensive.
My spouse is an audiophile, we have expensive equipment, and have a huge CD and vinyl collection. We needed to migrate our routine home and out-and-about listening to a digital solution. So, I digitized our enormous CD library to FLAC files, which are stored on an external hard drive connected to my desktop Mac. The files are backed up to another hard drive and also to BackBlaze.
I use Roon to serve the files to our HiFi system and our various devices. Roon offers a solution to make your library available remotely as well, but I don’t use it since I also use a streaming service. (We chose Roon because it obviated the need to tag all the files I’d digitized. It’s very good at scanning your library and serving up your files with all the metadata you could want.)
I use Qobuz as my streaming service.
A note: I started out using a NAS to store the music library, but frankly, it was more complicated to manage than it needed to be AND very expensive to back up to the cloud. My digitized music library is very stable, i.e., we never add anything to it. So, it’s just as easy and safe to serve the files from an attached hard drive which is backed up to the cloud and, from time to time, to another hard drive.
But here’s one thing I’ve learned: if I had to do it all over again, and if it were just me, I’d ditch the CDs and the vinyl without bothering to digitize anything and just stream everything. With very rare exception everything in my physical library is available on Qobuz in high-res files. I’ve found that I’m much more interested in discovery than I am in revisiting my collection, which was only as big as it was because there wasn’t an alternative. Compared to what I paid for physical media, and what I’m paying to store the digitized versions, streaming is a bargain with none of the cognitive overhead to boot. And here’s another thing I’ve learned: you can listen to great radio from anywhere online. If I really had to penny-pinch, I could fill my ears with ad-supported Spotify and streaming radio. (One of my favorites is WNYC’s New Sounds feed.) Obviously, if I had tweens and teens at home, I’d need something more.
As for photos … I’m a very serious amateur photographer (as in 10+ hours a week doing something with photography serious) and am more than happy to pay Adobe for Lightroom and Photoshop, both of which I use extensively. The only photos in the Photos app on my Apple devices have been taken with my “real” cameras, processed in Lightroom and/or Photoshop, and put there purposefully—i.e., I don’t need to pay Apple for storage because I simply don’t load much into the app. (I tend to take two kinds of photos with my phone: “Sketch images” of something I want to shoot later with a “real” camera and to capture information I would have written down with a pen in the past, e.g., part numbers and the like.) I don’t need what Apple Photos does since I process my images and manage my catalogue with other tools, and don’t really take the kind of photos it appears to have been designed for—a worthy category I’ll label “memories.”
I use Lightroom to manage my catalogue, but I don’t store my photos in anyone’s cloud. They live on an attached hard-drive, get backed up to a second hard drive, and are also backed up to BackBlaze.
You can use Adobe Bridge for free to manage your catalogue. I haven’t investigated the ins-and-outs of using the various cloud storage providers for photo storage and sharing, but both DropBox and Google are in that space. (But be careful: you may not be able to use either to view raw files.)
PS: the only Apple service I use, believe it or not, is Apple TV. I do pay for 200 gb of storage for mobile device back-up, but use DropBox for cloud storage and syncing.