Is it racist to call a European person a 'gr**go'

"Gringo (feminine, gringa) is a Spanish word used in Mexico and other parts of Latin America, generally to denote people from the United States, more specifically white Americans."

Why would it be offensive to Europeans then?

It's not only directed at Americans, it depends on where you go but often it just means (white) foreigner in general.

Would you be offended by it? Because I don't know anyone, non American, who would be.

No, not at all. I was just pointing out that not just Americans are meant by gringo