Maybe it's not fair or accurate to say conservatism and it's adherents are racist. Racism certainly cuts across political boundaries and includes white liberals too. However conservatism is problematic because it denies systemic racism, it benefits from backlash politics, and it envisions an orderly and decent society that tolerates racism. While there is nothing racist in philosophical conservatism, it's easy to understand why conservatives are called racist because of what they do.
Conservatives deny systemic racism thinking it ended with the Civil Rights Movement. That was only a start. Overt racism and legal segregation are no longer a problem, but subtle racism is real. It's how systemic racism works. This racism that still holds black people back economically, socially, and politically. Things like stop and frisk are not isolated incidents. It's official policy for how black neighborhoods are policed. Black people with the same credit and income as whites still pay higher interest rates on a home mortgages. These things happen all the time because it's how society works. Conservatives blame blacks for racial inequality. They cite culture and behaviors like crime, violence, fatherlessness, the decline of marriage, lack of academic engagement, and government programs that discourage work. There was a time when these things were less problematic among blacks, and we were not fully free or equal then either. Racism and an unfair economy put black people in abnormal conditions. It's wrong to expect them to live healthy, normal, decent lives under those circumstances. Conservatives know better to suggest otherwise, but their politics depends on not blaming an society.
Conservatives benefit from backlash politics appealing to white resentments and fears of racial equality. For some whites any progress by blacks is a threat. Conservatives knew this in the 1960s so they appealed to racism for political gain. They spread racist stereotypes about lazy black welfare recipients living off hard working whites' tax dollars and black criminals who threatened white lives and property. They did this despite the fact more whites get welfare than blacks, and blacks are more likely to commit crimes against other blacks than whites. Over the years this racial politics has become increasingly populist. The narrative goes like this - wealthy liberal elites in the media, entertainment, academia, technology, and government wrongly vilify working class whites as racists. The elites advance blacks at the expense of whites struggling to maintain their way of life and economic wellbeing. In this telling - busing destroyed white neighborhoods and schools in the name of forced integration. Affirmative Action took jobs and college admissions away from qualified whites in favor of unqualified blacks. Today these liberals preside over a global economy driven by technology, finance, free trade, and immigration that is destroying white jobs, communities, and culture. Meanwhile whites can't say or do anything without being labeled racist. At the same time blacks want reparations and to defund the police which liberals will gladly do. To these whites Donald Trump was a hero who fought back. He was their president. Trump was the man fighting the oppressive deep state and globalism that undermined ordinary decent white working Americans.
It doesn't matter that Trump and other rich people along with corporate interests rigged the economy to lower their taxes, pay workers less, destroy unions. They play the stock market taking risks they can't afford, and get government bailouts when markets collapse. These same people give money to politicians in both parties who cut safety nets and regulations that benefit the people. Conservatives appeal to racism and white victimology while doing things that undermine whites economically and socially. Meanwhile blacks bear the burdens of racial discrimination and economic inequality.
Conservatives opposed civil rights laws in the 1960s believing they were government overreach that threatened personal liberty and property rights. All the while they claimed to be against racism and believe all individuals should be equal before the law. What this did in effect was to prioritize the liberty and wellbeing of whites over blacks. It didn't matter to conservatives that legal segregation in the south and de facto racism in other parts of the country harmed blacks or deprived them of the equal right to liberty. This situation would not work itself out. Conservatives is clear about what should be preserved, but it's never sure about what needs to change.
They have too much invested in the past and too much to lose in the present by changing their views. The stable, orderly, moral, society conservatives believe is essential to human wellbeing is problematic. It allows injustice against blacks, and depends on the goodwill of whites to voluntarily treat blacks better as individuals. But the government shouldn't do anything because that would be unfair to whites. At the same time conservatives urge blacks to fix themselves morally and culturally. They say stop blaming white society or relying on liberal government to solve their problems. In this way conservatives let themselves and America off the hook. Conservatism is too important politically to go unchallenged when it comes to race.