If someone believes all white people are racist, does that suggest that that person is racist?

I think it could be argued that that person is racist because he or she applies something negative (racism) to an entire race based on their race. What do you think?

Yes, someone who believes all white people are racist should be considered racist.
No, that is not logical.
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If someone believes all white people are racist, does that suggest that that person is racist?
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