There's always the Amazon Appstore. And with an open-source Android variant, you could restrict apps that demand over-reaching permissions, including the Amazon Appstore itself.
The Amazon Appstore is trash, and many of the apps in it are out of date or outright nonfunctional. When I tried using Skype on my old Android phone, and it required Play Services, I was mystified because it was also available on Amazon.
As it turned out, the Amazon Appstore version was so out of date it just didn't work anymore.
