How do I set my Steam wishlist to public?

Go to https://steamcommunity.com/ and log into your Steam account; then, in the upper-right corner click on your profile name and select “View profile”:

Next, you want to click “Edit profile”:

In there, you want to go to “Privacy settings” and make sure “My profile” is set to “Public” and then “Game details” also to “Public”:

Other settings are irrelevant for the wishlist syncing. The settings are saved as you change them, there is no “Save” button.

Voila! You can now proceed with Kinguin sync Steam wishlist.