Problem:

Show a field from a related parent custom post in a product page (it's a book page and I want to show the authors information).

I deactivated all plugins and changed theme and it worked

Solution:

It should be a compatibility problem between Toolset plugins and other plugins/theme in your website, I will not be able to duplicate same problem with only the database dump file, as I suggest you above, please try these:

1) deactivate other plugins and switch to wordpress default theme, and test again
2) If the problem is fixed, please activate other plugins/theme one by one, try to locate the problem plugin or theme

Relevant Documentation: