If your site is hosted on WP Engine, you might need to ask their support team to exclude certain pages from caching, when the content on those pages is dependent on the group memberships of the current user.
For example, if you use WooCommerce and restrict certain products to users who belong to a group, then the product category pages might need to be excluded from WP Engine’s Page Cache, so that visitors only see those products in a category that they have access to.
See Effective Cache with WooCommerce for details on the default exclusions that are applied.
Based on the above, if you are going to contact WP Engine’s support team to exclude certain cases, you can refer them to this page when submitting your ticket.