Hint: it’s classic “politics is not about policy”.
First, it has nothing to do with actually liking Black people. Leftists, as a rule, disdain Clarence Thomas more than if he’d been in prison for shooting some store owner. If conservatives weren’t generally sensible on this issue, they could easily and freely accuse the Left of racism for fun and profit for this alone. But they don’t, and they won’t. Because this game is insulting to the intellect.
Second, it has nothing to do with policy. Despite feigned concern for “muh poors and browns”, there is virtually no evidence Blacks perform better under Black-run governments, and much evidence to the contrary -quick, can you name a Black-majority First World country now? There’s only one of them, and its GDP per capita is lower today than in 1969, before its independence from a White-majority country. Fewer Blacks are killed by Whites each year throughout the world than are killed by suicide and heart disease.
Nobody believes Louisiana and South Carolina will re-enact Jim Crow, deny voting rights to Blacks (except by racially blind and futile means), or even abolish affirmative action if the rest of the country disappears. Nobody except the truly deluded believes having the least racist police force in the world -or none at all- would ever prevent a greater percentage of Blacks from committing violent crimes than Whites. Nobody believes more than 10% of Americans would admit to being racist under any reasonable circumstance.
So what could be the reason for this condemnation of patriotic Americans as racist? To answer this, imagine if you went up to your typical progressive and claimed with the utmost seriousness that you were a racist, that you did not think Blacks ever deserved or ever could deserve the right to vote, and segregation was a right and proper means of preserving a civilization-affirming modal Black culture in the pre-civil-rights era South, and that there was nothing wrong with some states deciding to keep themselves free of the scourge of Blacks and their criminality. What would the reaction be? Probably utter shock, if not an immediate shunning of you and all your allies. Now, why would that be? Again, it’s been ascertained your typical progressive does not care much about Blacks at all. It must be a matter of social status-signaling. By saying “Black Lives Matter”, the progressive is not saying “Black Lives Matter”. He is saying “I am humble in the promotion of the ambitions of people of my race, and, thus, myself; I am a true altruist in the manner of the Early Christians; I am willing to destroy the world so that all men be made equal”. In the end, this really comes down to Nietzsche and his idea of herd-morality, the desire to gain one’s status as morally worthy via submission to others rather than yourself; from self-flagellating, rather than self-affirming. If the world was made rational and utilitarian, almost no attention would be paid to White assaults on Blacks, and segregation would be on the table as a discussable option to reduce the threat of Black crime to innocent White victims of it (like me).
Now, as for why progressives falsely accuse conservatives of being racist, that’s just due to their desire to exaggerate the degree of evil in the world so that they look more virtuous. If there were no racists out there, no progressive would be satisfied. In fact, they would be very dissatisfied, indeed.