Is capitalism the cause of racism? Of course not.
Racism has been around for thousands of years. Capitalism has only been around for a few hundred -- details depending on interpretation. So obviously racism can exist without capitalism.
I say racism has been around for thousands of years. Here is what I mean. I think the best understanding of social systems before either capitalism or feudalism comes from the ideas of Maoist theorist Samir Amin. (That's not to say that I agree with his Maoism. I don't. But we learn from whom we can.) On his understanding, settled societies before about 1000 AD, and some after, were "tributary" societies. This means that a dominant tribe obtained tribute from subordinate tribes by means of openly coercive, violent threat, without any pretense of mutual benefit. Despite the term "tribe," many of these societies were urban, and the dominant groups were city-dwellers -- Rome, for example, from whom we get the words "tribe" and "tribute," from the same root. Other instances include the Greek city-states and the Muslim caliphates. In these societies slavery is common (Marx and Engels called it the slave system) and slaves are often themselves tribute and are commodities in trade. Racism -- the socially-constructed superiority of one group or another, by skin color, religion, language or dialect, or other ethnic characteristics -- is essentially necessary to a tributary system, as the dominant tribe claims entitlement to tribute on the basis of its supposed superiority.
When newly expanding capitalism encountered tributary societies, "western hemisphere slavery" and colonialism were among the results. In both cases, capitalism adapted itself to the forms of the tributary societies, but turned them to the capitalist purpose of making money. Essentially, the (European) capitalist adventurers bought the role of the tributary superiors much as inbev is buying SABMiller. Since racism was a means of maintaining the purchased enterprise, it was intensified, to increase the profits.
(Of course, ethnic prejudice was not new to European cultures, some more than others. The attitudes of the English toward Celts and of many Europeans toward Jews were easily transferred to the new setting.)
So, no, capitalism is not the cause of racism. In an ideal version, capitalist economics is based on unchecked competition, which would seem incompatible with racism. But capitalist politics makes it very difficult, perhaps impossible, to get rid of racism. The reason for this is one that Bernie has made familiar: the capitalist class are few -- the richer, the fewer -- and if they are to influence the political system, they need to divide the working class. To do that they will use whatever tools are at hand. Thus, where-ever we see capitalism, we see hatred of an oppressed group -- in Europe, antisemitism and hatred of the Romany. This is a tool that got out of the control of the capitalist class, even to a greater extent than anti-black racism here in North America has sometimes gotten out of control. In Japan, hatred of Koreans and their former slave class.
This leads me, along with many socialists of all sorts, to the following conclusion: unless the working class can unite, black and white alike, there is very little if any prospect of a politics that can confront and eliminate racism. As long as it is in the interests of a small but influential class to divide the working class, racism is a tool they will use. The only way to take the tool away from them is to take power away from them. The way to do that is to unify the working class around the common interests of the working class.
Conversely, this sort of unification cannot occur unless the white working class comes to the support of "black issues." Black lives matter! and they are endangered, today, in ways that white lives are not. The billionaire class has no more useful tool than a white worker who takes pride in being "better" than people of color just because he is white, and so opposes "black issues." The message -- "vote according to your economic interests" -- is addressed to him or to her. Nothing is more certainly in the economic interest of white working people than the security of people of color, because that is necessary to the unification of the working class, the rebuilding of a union movement, and real democratic political power.
That is why we democratic socialists do and will support black issues, not as something separate from our economic program, but as an integral part of it. It does help that is is anyway the right thing to do.