I like that Romney gave a speech on religion in America, and I liked the overall direction of the speech which seemed to support the classical liberal view of secularism.
Unfortunately he made several statements that dramatically detracted from the speech. The most powerful part of the speech was the statement "Freedom requires religion just as religion requires freedom."
Unfortunately, the powerful statement is clearly a fallacy. History is full of totalitarian states that used religion to cement in the fealty of the people. He probably made the slip simply because he was not taught logic in school. These days, no-one is taught logic; so we've come to expect such fallacies.
I suspect that Romney was trying to make an argument similar to the argument that you can't separate faith and reason. Science is built on a belief that there are discernible physical laws. Faith is meaningless unless you have some sort of logical method to act upon faith.
You can argue that there is a dependency between faith and reason. Freedom and religion go well together, but aren't dependent on each other.
It is possible that Romney was referring to the Mormon doctrine of "free agency." Free Agency is something different from the common usage of freedom. If he was using a definition of freedom that is specific to his Church, then he blundered by not explaining to us that he was using a stipulated definition.
Either way, including a statement that most people would see as a logical fallacy in a major speech shows a disturbing lack of judgment.
The public schools may not teach logic, but we still get upset when our leaders make blatant logical fallacies in major addresses.
The biggest gafaw was to put the statement "A person should not be elected because of his faith nor should he be rejected because of his faith" in a speech about the importance of faith.
I agree that a candidate should not be seen as a spokesman for their faith. Nor should they be judged for all of the silliness of a church's theology. The public should grill a candidate on any belief that might affect a candidates decision making process.
We can find a good example of a religious tenet making a member of the faith a bad presidential candidate in a religion called the Hutterites. The Hutterites are fanatically against the use of violence. They are so thoroughly opposed to violence that they conscientiously object to serving in the military.
The President of the United States is the Commander in Chief of the United State's military. Even though I respect the non-violence convictions of the Hutterites, I would probably reject a candidate whose religion would prevent him from serving in the military that he must lead.
The vast majority of theological disputes should be checked at the door steps of the Capitol. However, any tenets that affect the functioning of a candidates fulfilling of their position should be up for debate.
Religion shouldn't be a test. However, we are wise to discuss how faith affects the decision making process.
If faith matters; then people should reject a candidate when they have substantive objections to how the candidate's faith would affect their performance in office.