Selfhosted

Hmm, I don't know anything about Whoogle, but from other privacy-conscious search engines, I would expect it to work when you use that URL in your bookmark.

Three things I can imagine:

• Something in your hosting stack strips the URL parameters, like maybe your reverse proxy, if you use one. You might be able to see in the Whoogle or web server logs, which URLs actually reach it. Might need to set it to debug/trace logging.
• Maybe there's a flag in the Whoogle configuration you need to enable to accept these preference URLs.
• It's a bug in that Whoogle version.

It says right above that box that it requires the WHOOGLE_CONFIG_PREFERENCES_KEY or that option will be ignored. My guess is that you have to manually edit some config file to turn that key on, or generate an encryption key yourself that you provide through editing a config and adding it to that line.

Edit: you probably need to add your own domain or IP as the root URL too.

One alternative is to us SearXNG for similar functionality. The preference tabs work for them. I am using northboot.xyz and adjusted the colors and default engines but you can pick anything from searx.space