Is disabling built-in apps fine?
Most apps on android are safe to disable, however some can have some pretty bad side effects.  This however depends on what your needs are. You can disable the camera for example but it will also disable the gallery (at least as of kitkat and I believe Lollipop is the same way).

Android does have some core applications that are essential to the function of the actual system itself. For example disabling Package Installer will disable the ability to install any application and will likely cause your phone to go into a boot loop/soft brick. 

More to the question, if you are unrooted you should be relatively safe since I can't recall any application without root privileges that can access and 'take down' any vital apps on the system.  That being said going mucking around with the core applications that make your phone/tablet function shouldn't be done lightly.

Source: I build custom roms, and I am a former PAC ROM maintainer.