In the late 19th century, this political and social movement swept through the United States, its followers believing that all people who were not born in the U. S. and were of European heritage should be banned from the country.

The correct answer is Nativism

Explanation:

The policy of  Nativism is of political nature which relates to promoting the interests of native inhabitants against those of immigrants, including by supporting immigration-restriction measures.

As per the definition of this policy the followers believe that it is the birth right of the US borns to stay while the people who have migrated to US should be banned.