I believe J.K. Rowling was married in the Scottish Episcopal Church by the Rev Canon Prof J S Richardson. But if she attends the Church of Scotland, well, that’s quite interesting - the Church of Scotland has no bishops, unlike the Scottish Episcopal Church which does. The Church of Scotland is Presbyterian - John Knox and all that.
She went to a Church of England school when she was young, but I’m not sure it was the happiest of her experiences. The former Archbishop of the Scottish Episcopal Church was pretty radical - much more in line theologically with the American Episcopal Church. In fact, the Scottish Episcopal Church is very much like the American Episcopal Church in theology and politics. It is very progressive. The same cannot be said for the Church of Scotland.
There are also some cultural differences between to the two churches, especially in relation to the Scots (and their relationships with the English, even to this day). These cultural differences are in addition to the theological and political differences between the two denominations.
The Scottish Episcopal Church has been very involved in progressive Scottish national politics - in fact, I think it was one of the sponsoring institutions to bring about the creation of the Scottish Parliament. The Scottish Episcopal Church, from the witness of my friends in Scotland, is fairly burned out and no match for the descendants of John Knox. In fact, one of my friends attempted to go to the local Scottish Episcopal Church but she was a little late and the vicar had locked the front door, even though it was Sunday. His view was if you weren’t there on time, you should go somewhere else.
My guess is still the play is on the first name - Pius (said satirically) - and his “false piety” made him blind to the evil around him, even weakened him to be used by those he should be opposing. That certainly is a problem in the Church today.