Extend core modernizr library
I'm pretty sure you have to override core/modernizr with a later version in order to get objectFit. 


Download an updated modernizr.js and include objectFit. 
Place the file somewhere in your theme's path (js/ or scripts/)
In your theme's info file (theme-name.info.yml) , override the existing modernizr library


libraries-override:   
  core/modernizr:
    js:
      assets/vendor/modernizr/modernizr.min.js: scripts/modernizr.js


You should now have access to objectFit.