As Barcelona becomes increasingly multicultural, particularly in areas of the Old City such as El Raval, visitors and residents of all nationalities are naturally accepted by a fairly open-minded society. A person of a different race or skin color rarely draws even a second glance, unlike a few decades back when Barcelona was a 99% castizo (locals) city.
That said, instances of racial conflict are not unknown, though these tend to be with African, Arabic, and Latin American locals rather than foreign visitors.
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