Encrypt all the things!

Facebook, in theory, doesn't have my phone number (don't use the phone apps and have never given my number to Facebook).

Would this stop the ability to link the two accounts or is it done through other ways?

The vast majority is done via your mobile phone apps installing the Facebook SDK for Facebook login integration. Even if you don't have a Facebook account or have logged in using one... the SDK pings info on every app startup, and some apps choose to integrate deeper.

Things that can build an advertising profile:

• Mobile app ping your identity and/or IP address (correlate on IP address and device fingerprint - maybe associated to an actual email)
  
• Email addresses being used the same across multiple apps (correlate on email)
  
• Phone numbers
  
• Your contact list (i.e. in WhatsApp... the map of connections is a form of identity)
  
  

Everyone has a Facebook advertising profile... all you can meaningfully do is minimise how enriched it becomes, and if you're very successful you may prevent them from correlating too much together (in which case you have lots of sparse profiles).