There are YouTube clients which work on Fire tablets without Play Services. Also can use Silk Browser to load it, log in and use. I do that same browser trick on my ancient Samsung tablets as well. Zero dependence on Play Services since you're just using a browser cookie.
Maps will work without Play Services, but it just pops up a notice or shows a triangle error notification about it, but those can be disabled/tapped through. No account data is saved but navigation works fine. Also, many ancient versions of said apps pre-dated Google integration since they were back in the Android 2.2 days before it became a thing. (they also lacked Google branding, just called Maps, Books, Music, etc)
A lot of apps that claim to need it also will work, a game called Wheel of Fortune works but will pop-up a notice saying it won't, just tap outside it and it works fine. Other apps might fail to get location since they use the Location API in Google Services, but you can add location in manually (such as weather apps). Google Chrome will also work, just disable all notications in settings to get rid of the persistent 'Chrome will not work without updated Play Services' notification.
Also there are things such as Micro-G, an open-source Play Services alternative to make apps that outright refuse to work run, and YouTube Vanced, a Google-free implementation of YouTube. Custom ROM and root users have been aware of this for quite some time.