I tested your code and the generated link (and associated rewrite rule) for the taxononomy is:
/products/training-outfit/
not
/shop/products/training-outfit/ (which creates a crazy query)
Did you create any rewrite rule to obtain this result?
Also it is not clear to me if you activated or not the translation for your custom post types and taxonomies. In my tests, /products/training-outfit/ works if I activate the translation. There is still a bug if the translation is not activated.
Maybe you should also look a these plugins (if you don't have theme yet) to help you debugging this issue:
debug bar
debug bar extender
rewrite rules inspector