This is the official policy, but everyone knows it's bullshit. Using post WW2 changes as an example, we quickly forgive countries that Americanize (such as Japan), while we quickly forget allies who veer off on their path (such as Russia). We overthrow democratic governments who oppose us and bring back monarchs who are on our side (such as in Iran), while we prop up oppressive monarchs who support us (such as in Saudi Arabia).
And I recognize the fact that it's offensive to transplant our culture/values, which is why I think it's best to just try to bring those people who already agree with our culture and values to America. Let the extremists kill one another - we just need to get the bystanders out of the way.