The phrase "separation of church and state" is not in the Constitution. It says Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof. The Free Exercise of Religion Clause of the First Amendment is a prohibition on Congress, period. A priest denying communion to someone can't possibly be a violation of a prohibition on Congress (or state legislators since it applies to the states as well).
Think about how upside down this idiot has things. She is claiming that the Free Exercise of Religion Clause of the First Amendment of the Constitution requires the priest to violate his understanding of his own religion, i.e. prohibits him from exercising his religious beliefs. If anything, the Democrat calling on the priest to resign is arguably in conflict with the First Amendment than anything the priest did, since she is a lawmaker, whereas the priest is outside the government. Of course she was only exercising her free speech which is also protected.
We are in agreement. You said it much better than I could.