I believe that racial breakdowns in visitorship is a highly local issue.  For
example, I would expect visitorship by nonwhite races to be higher in New York
City than in Hudson, Ohio.  Also, the breakdowns would depend on the mission
of the institution.  For example, the Studio Museum in Harlem, which exhibits
work by Blacks, is visited mostly by Black Americans.  The Museo de Barrio is
likely visited largely by Latinos.  The Guggenheim is largely visited by
whites.  Also, at The Skyscraper Museum (NYC) where I work part-time  we saw
our Black American visitorship rise when we exhibited the pencil artwork of a
Jamaican man.  Consequently, visitor counting by race is also partly dependent
on what is exhibited.
        This question is complex, I believe.
Mike Radice
The Union Institute