Problem: Non logged in users can access a category page though the CPT is set to private
Solution: You can use the pre_get_posts action hook to disable the taxonomy term archive.
You can find the proposed solution in this case with the following reply: => https://toolset.com/forums/topic/non-logged-in-users-can-access-a-category-page-though-the-cpt-is-set-to-private/#post-1799989
Relevant Documentation: => http://jboullion.com/disable-taxonomy-archive/
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