That statement is probably not true, and would be next to impossible to prove. I will grant you that nine out of ten members of a lynch mob attacking a black where more sympathetic to the Democratic Party than the Republicans.
Ill bet theres no indication of the fact that no black person was ever lynched by a Republican.
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However there is much documentation of Republicans and even teachers who dared to teach blacks, being lynched in the south’s Jim Crow era.