No, I'm not joking, my confusion stemmed from the fact that those who used those terms always seemed to mean them in the way I described. (Probably mostly Americans who grew up with the two party system)
In Germany - at least in my bubble - we don't talk about "liberals" vs "conservatives", the spectrum is more diverse.
Not a parent, but I was raised bilingually in English and German, while growing up in Germany.
My Dad (almost) always speaks English with me, and my Mom (almost) always speaks German with me, even to this day at age 31. This approach worked well for us and I'm fluent in both languages, but I can imagine an approach where both parents speak both languages could work as well.
What also really helped me was to consume a lot of media in English, so maybe you could encourage your child to do that as well.