Hey Luis! Thanks for bumping back 
Once I created the component, I did not change the settings, only styling, but:
I had my head around that several times during weekend. I tried recreating the component several times - deleted the component, disconnected the app, deleted the interactions, cleared cache, published again, connected the app, set the options, created the component, set the cookie scripts.. and I noticed that the problem persisted when I used custom toggles option.
This morning, when I cleared the unused classes after deleting the component, there was still fs-consent_prefs_checkbox, fs-consent_prefs_checkbox 2… 3 … etc classes that were not cleared, but in the same time they were not traceable anywhere, on any page, any component etc.
I renamed them to dummy class names x, y, z etc, connected the app again and created the component, now trying it without the custom toggles.
Now it seems to be working.
Was a bit annoying because I had to reschedule the pre-launch client meeting we planned, cause I wanted to make sure it will be working properly (the client is a therapist and relies on GDPR compliance critically).
We would love to launch the website this week. I prefer custom toggles over classic checkboxes, hope you can guys make it work somehow.
Cheers from Norway! 