Since she mentioned only schools run by Catholics, Jews, Muslim extremists and white racists, I can only assume that Hilliary believes schools run other Christian organizations would be included in the latter category.
In fairness to Hillary, there are very few private Protestant schools in NY (one exception that I can think of is "Friends Academy). Most of the private schools are Catholic, Jewish, Muslim or secular.
Even if your assumption was correct or even if Hillary admitted that.She would never get called on it.