For hashtags that are on private account I would think if I am following the account with the account that I am logged in with, the pictures would not be private to me and would show. This is not happening.

Hey Faris!

Kindly note, that Instagram API does not allow pulling images from private accounts. So unfortunately Instagram Feed WD plugin cannot get them and that is why you are not seeing those images, even if you are following the user.

Thank you!