Profile: nelsonT-2

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/