Hello, @marzio.biancardi@gmail.com,
To solve your issue, first of all, I disable all the third-party plugins on your site see the image: https://postimg.cc/HJb9Kjv7 by doing this the variations start to appear on the single product page but not on the shop page infect the theme options were set to ok. Then I check the attribute type on your site from the Dashboard >> Product >> Attribute >> edit attribute check the image: https://postimg.cc/ZBVptN80, before the type was chosen to the “Select” and Select type of attributes, does not appear on the shop page so I changed it and now here is the result of shop and product page on your site: https://postimg.cc/jWhJPfkv and https://postimg.cc/9zkwdCJ3 Please check back to your site after clearing the browser cache.
Note: Now, you have to enable the third-party plugins one by one on your site so that you will be able to know which plugins conflict and cause the issue.
Regards 8Themes Team.