The music player, the messaging app, the home screen ... these are not part of the operating system and are easily replaceable.
I actually have an older phone (a first-gen Galaxy S) on which I installed Cyanogenmod without Google's services, which is basically stock Android. In spite of opinions to the contrary, the phone is quite usable without any of Google's services on it.
I've got Firefox for web browsing, OsmAnd for maps, Apollo for playing music. All 3 are open-source apps. At some point I even installed Amazon's App Store on it, to be able to get some proprietary apps, like Facebook, installed. But then I realized I don't need all that bloatware, as the web versions work fine.
You should try out this experiment if you've got an extra Android lying around. After you find apps suitable for whatever it is you want to do, it really is OK. The level of polish is not the same as with the Google-enabled Android, but it's still much, much better than the experience you get on low-budget non-Android smartphones.
People forget that Amazon already forked Android and that without Android they wouldn't have been able to deliver Kindle Fire. That's the power of open-source, even if you choose to deny it.