Potter is a not uncommon Muggle surname, and the family did not make the so-called ‘Sacred Twenty-Eight’ for this reason; the anonymous compiler of that supposedly definitive list of pure-bloods suspected that they had sprung from what he considered to be tainted blood.
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Henry caused a minor stir when he publicly condemned then Minister for Magic, Archer Evermonde, who had forbidden the magical community to help Muggles waging the First World War. His outspokenness on the behalf of the Muggle community was also a strong contributing factor in the family’s exclusion from the ‘Sacred Twenty-Eight’.