I'm sad to say that at this point in time the answer to that question is 'yes'. Today all Republicans are, in fact racists. Yes, there are some people who call themselves Republicans who are not racists, but they aren't actually Republicans, they are RINOS, Republicans In Name Only. And it is specifically their lack of racial bigotry that has caused the new Ultra-Right-Wing leadership of the Republican Party to give them the boot.
Strange are the twists and turns of history and sociology as one party slowly drops the white hood of racial hatred and another picks it up.
Of course we know that 'all Republicans' weren't always racists. After all, Abraham Lincoln was a Republican at a time when that party had a northern base and the Democrats with their southern base were the racist party. But that all changed over time. After the Civil War Democrats began to broaden their base and eventually, by the 1950s and '60s the Democratic Party was home to great civil rights leaders. This was an uncomfortable fit that didn't last long. The progressive civil rights stance taken by presidents JFK and LBJ was more than the racist southern Democrats could stand and when LBJ left office, their mass exodus from the Republican Party commenced.
The lilly white MLK hating Richard Nixon won the presidency in 1968 and it would have been a landslide except that the more extreme racist George Wallace ran as a 3rd party candidate and took over 13% of the vote.
George Wallace would have a near death-bed conversion and he later renounced his racist views. But many other white people would not see the light and it is those hate-filled evil bigots led by Limbaugh, Hannity Glenn Beck, Mark Levin, Ted Nugent, etcetera who have won the hearts of the Republican base. As I said before, there are many non-racist people who still call themselves Republicans, but just ask Ted Cruz and Rush Limbaugh, those people aren't Republicans, they are Republicans In Name Only.