Can I safely use the same UUID on independent sites?
This is a perfect use case for Features. You can export shared sets of functionality and configuration without worrying about UUID stripping or collision.


  The features module enables the capture and management of features in
  Drupal. A feature is a collection of Drupal entities which taken
  together satisfy a certain use-case.
  
  Features provides a UI and API for taking different site building
  components from modules with exportables and bundling them together in
  a single feature module. A feature module is like any other Drupal
  module except that it contains additional information in its info file
  so that configuration can be checked, updated, or reverted
  programmatically.
  
  Examples of features might be:
  
  
  A blog
  A pressroom
  An image gallery