bobsp: Some bug prevent to add or remove game from the wishlist : when looking in Firefox debugger, I see the wishlist https request receive "401 Unauthorized" response.
I also see a lot of warning/errors in the javascript console. Did the gog.com frontend developper never check their code before release ? :-)
The wishlist works fine for me here. I also use uBlock Origin, NoScript and other browser addons (which are not firewalls BTW), and I've never had uBlock Origin ever block anything on GOG. NoScript on the other hand depends on if and how you actually use it (how strict you have it set up), and if you permit all of the necessary GOG subdomains (which can change and have new ones over time also) permitted to work or not.
Despite all of that, wishlist is working fine here. If you're getting a 401 unauthorized error however, that has absolutely nothing to do with your web browser or any addons you might be using, that is a direct error from the webserver, which probably means it is under maintenance or something. Refresh the page a few times or wait an hour and try again.
Also worth noting is that problems with websites like GOG may happen for one person or several, but not everyone, and just because it works for some people (such as myself) does not mean it should guaranteed work for you. GOG and most other major websites use a content delivery network which is a farm of hundreds or thousands of servers spread around globally, so the chances of 2 or even 100 random people all getting content served to them from the exact same physical computers is about the chance of winning the lottery jackpot. If one server in one datacenter in one country goes poopsies, that will affect some number of people within that region only, and not affect anyone else globally.
If you continue to have problems like this persistently with the wishlist, contact GOG support with the link at the bottom of the website homepage. They can investigate the issue without guesswork and random theories.
Hope this helps.