You can always apply to programs at state universities where the states have rules against use of race/ethnicity in admissions. For example, AZ, CA, FL, MI, NE, OK, TX, WA.
However, graduating from such a state university will not prevent people from making assumptions if they are prone to doing so and your race/ethnicity is visible to them, since there have been instances on these forums where posters assumed that state universities in those states were considering race/ethnicity in admissions when they actually were not.