A person who is obsessed with British culture is an Anglophile. Is there a word for a person who is obsessed with American culture (that is, the United States)?
Americanophile, according to Merriam Webster:
a person who greatly admires or favors America or things from American culture
The word is also listen in the Oxford Dictionary Online.
Attribution:"Americanophile." Merriam-Webster. Accessed April 09, 2018. https://www.merriam-webster.com/dictionary/Americanophile.