Plenty of people have a strong dislike for Catholic schools when it comes to high school sports, and that's the extent of it. Most of these same people who dislike Catholic schools (and vice versa) would still not think twice about helping someone out with a flat tire, paying it forward in a starbucks drive thru, holding the door, doing business, or any of the other thousands upon thousands of normal decent human everyday acts based off of a someone's high school athletics allegiance. Anyone who actually holds on to true emotion that effects their everyday well being based on a high school athletics contest (small number on BOTH sides), there's no helping those people.
The whole public/private thing is such a waste of thought. There are so many grey areas for each side, your extremists on each side, your outliers on each side, etc...
It's definitely a 2 way street. And I'm happy to live in a country where my biggest stressor of the weekend is a private school beating a public school in teenage football. Like I've said before, these are 1st world problems.