Hi!
A note on my previous comment: it doesn’t work in Firefox either, I realized that it only works when you have a product added to the cart, so when I tested it I had a product in the cart in the Firefox browser.
I tested it in the Chrome browser adding products to the wish list and in the comparison list, when visiting the page it says it is empty. But just add a product to the cart and the products appear in the wish list and in the comparison list.
Note: My caching plugin is disabled.