Profile: Michael

Problem:

I want to let users select a custom post and save it. Like adding a product to a cart, only they're simply saving posts to their profile.

Solution:

I suggest you try to create a custom post type, and connect it with your posts, for example:

https://toolset.com/forums/topic/how-to-save-custom-posts-to-user-accounts/#post-1158540

Relevant Documentation:

https://toolset.com/documentation/post-relationships/