It's not about the relationship between a parent and child being affected. It's about that child's relationship with GOD. If there is even a risk of negatively affecting that, then it's not worth it.
In Mark 9:42, Jesus says:
“But whoever causes one of these little ones who believe in Me to stumble, it would be better for him if a millstone were hung around his neck, and he were thrown into the sea."
So, if you teach your children about Jesus Christ and Santa Claus on the same day every year, then eventually your children discover that you've been intentionally lying to them all along about Santa Claus, then how do you expect them to react to Jesus Christ? All you are doing is compromising your witness for Christ, which is more important than any temporary happiness they might get from believing in Santa Claus.
The primary purpose of parenting is not to provide a happy childhood, or a good education or produce productive members of society. Those are all good short term goals, but they are not the ultimate goal for which GOD initially designed parents. The purpose of parenting is to raise children who love GOD first and foremost. Everything else is secondary (even buying a house at the age of 21). So, with that in mind, how can any CHRISTIAN PARENT possibly defend the practice of lying to their kids about Santa Claus? Well, they can't, the practice is absolutely untenable from a Christian standpoint.
Train up a child in the way he should go,
And when he is old he will not depart from it.
Nothing in there saying that it's okay to tell a few little, "harmless" lies along the way.
Originally I asked those Christian parents, who allowed their children to believe in Santa, to present some Bible verses defending that decision... still waiting on those verses.