If there's Biblical backing for a particular tradition then maybe it's worth getting wound up about. If there isn't, at minimum it probably isn't important enough to get real invested in from a religious standpoint. Even if it is a family tradition that you enjoy.
Isn't there at least equal incentive on to prove that long-held and beloved traditions associated with Christianity are valid regardless of the facts?
Maybe. But the point is a lot of people have an incentive to make these things out to be pagan, and they're on both the skeptical and the believing side. So you have to choose your sources carefully. Additionally, the vast majority of people aren't going to read a bunch of obscure, ancient writers (or even recent historians) to know who Mithras was, or how eggs were (or were not) used in pagan worship, so most people are getting these things 2nd or 3rd hand.