Dequeue Backbone from theme load and load CiviCRM Backbone
Assuming the file you want to load is the one located in the CiviCRM plugin folder at 'civicrm/packages/backbone/backbone-min.js', then you'd use:

wp_enqueue_script( 'your_backbone_handle', CIVICRM_PLUGIN_URL . 'civicrm/packages/backbone/backbone-min.js', array(), CIVICRM_PLUGIN_VERSION );

See https://developer.wordpress.org/reference/functions/wp_enqueue_script/

The only slight issue with this is that the constant CIVICRM_PLUGIN_VERSION is not updated with each minor dot release (it should be) which means that you may need to manually bump this each time you upgrade CiviCRM in case it ships with a new version. Replace it with your own version numbering in that case.

Disclaimer: I'm not sure if this is the only Backbone-related file you need to enqueue. Also, this may not solve the issue with your theme but it is the method by which you should target CiviCRM's copy of Backbone :-)