Everything voids warranties. If you are driving a new car, ie one still under warrantee, then you have to do whatever they want you to do. But there are lots of little myths about fixing cars, stuff leveraged by mechanics. Telling people that a diff will "blow" should the tires be 0.1% different in size is one of those myths. The entire purpose of a diff is to allow wheels to turn at different rates, hence the name differential. Only when you are getting towards differences enough to trigger anti-slip mechanisms during normal driving would it become an issue.

The manual probably also says that aftermarket oil/air filters will void warrantees, or that changing your own brake pads is dangerous. Total bunk.