Short Answer: It depends
Medium Answer: Yes, they are generally recyclable because pizza boxes average a grease content of 1-2% by weight and paper strength loss is minimal for concentrations <10%.^[https://recycling.dominos.com/static/media/grease_cheese_study.bc031166107ef14414e2.pdf] However, many municipalities prefer to play it safe. We should start having a discussion about this and encourage the development of paper mills capable of processing slightly more soiled material.
This isn’t a matter of whether one should disregard municipal recycling guidelines, but to encourage discussion on the current state of cardboard recycling in the U.S.