When did the Republican Party become the party of racism?

They aren't. Civil rights icon Dr. Martin Luther King was a registered Republican, the first black Congressmen were republicans, and most of the greatest strides towards ending racism were led or enacted by Republicans. By contrast, the KKK was originated by Democrats, the last KKK member to serve in Congress was a Democrat (Sen. Robert Byrd), and the Civil Rights Act was opposed by Democrats almost unilaterally. The thought that Republicans are racist is a result of the Democrats' efforts to secure the vote of minorities, starting with President Lyndon Johnson infamously declaring that "I'll have those nrs voting Democratic for the next 200 years." when it came to his efforts in creating the "Great Society". Since that time all Democrat efforts have been towards alienating the minority vote from the Republican party, which has been successful to the point that a majority of minorities believe that the party that freed the slaves, championed the Civil Rights Act, and led the way to equality in America is the biggest enemy to minorities today.