The white men already had the right to vote previously. The "grandfather clause" basically said that this situation didn't change. Any restriction on voting rights - which were of course specifically designed to have less black voters - was applied only to people who hadn't been able to vote previously.
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The couldn't vote if their grandfather had not allowed to vote
They could not vote if their grandfather had not been allowed to vote.
They couldn't vote if their grandfather hadn't voted.
They could not vote if their grandfather had not been allowed to vote.
Negroes.