If it were stupid as you suggest, would she have quit the church just before running for president? No, she wouldn't have.
It might not bother you that her (ex-)church calls the leader of the Roman Catholic Church the Antichrist but as theological condemnations go, that's as bad as it gets.
The fact is she was a member for years, she felt it contentious enough to cut and run, not unlike Obama throwing Jeremiah Wright under the bus in 2008.
As president of the United States how do you engage a religious leader, an ally, who is also a legitimate head of state, when your faith says he's the Antichrist?
She put it on the table by making her evangelical faith a cornerstone of her campaign.
Your points are valid.