Can you paint a clearer picture of the mechanism for federal intervention being the driver of intolerance?
When something affects you personally because it is forced on you it is much harder to be tolerant.
If it only affects the people who want that law then it is much easier to just say "I do me, you do you".
Different states are supposed to have different ways of life based on different value systems. That way people can move to the states that are most in alignment with their values. Laws at the Federal level take that freedom away.