Racial/etchnic tensions didn't begin in the U.S. with slavery, didn't end with the abolition of slavery, and since tensions exist all over the world, it won't end in the U.S. anytime soon.
You're trying to analyze a very complex issue by adjusting just one variable.
If you go read up on the New York gang activities of the mid 1800s you'll find that anything that could justify a person being excluded was used to rationalize every effort to exclude them. People wanted prosperity/security/opportunity/power (what name you apply here isn't that relevant). The Irish hated everybody because they wanted to protect their jobs and political power. Everyone hated the Jews because people have been hating the Jews, Hebrews, and Israelites for 3,000 years and old habits are hard to break. Everybody distrusted anybody who didn't speak a language they understood (usually English). The U.S. was one of the few immigration-oriented mixing pots to come to be in a very long time — and the nation was just begining to figure out how to solve some very old problems.
Free blacks simply added to already existing racial and ethnic tensions that boiled over at the time of the U.S. Civil War. Enslaved blacks were one of several causes that led to the devestation of the Southern Confederacy during the Civil War, and they were a very easy group to blame for their misfortune. How would any of this have changed if the U.S. had avoided institutionalized African slavery? It wouldn't have changed a single thing. Nada. The hate, the anger, the fear, the contempt, all would have shifted to someone else.
And often did. I can't prove it without doing some research, but I wouldn't be at all surprised if more Native Peoples died as U.S. colonialism moved west than did African slaves.
So, what would have changed in the 50s, 60s, and 70s if we didn't have the black civil rights protests? At that same time we had ERA/Women's Rights, we had Native People's rights, and a growing Latino sub culture in the U.S. Had institutionalized slavery never existed, we would have had immigration from African nations just as we did from all other nations, resulting in a growing African subculture. What would have changed?
Absolutely nothing. The historical claims of the cause of the civil rights movement would differ, but there would have still been racial and ethnic tensions resulting in various civil rights protests, violence, and change. At most, it would have delayed changes in law that had been boiling in the wings for 50+ years.
The point I'm making is that with every wave of immigration the "established" people in the U.S. have complained about the "new" people, resulting in tension. People hated the influence of the Irish in the early 1800s. They hated the influence of the blacks in the late 1800s and early 1900s. They hate the influence of the Hispanics today.
So, other than possibly (possibly, not accounting for natural immigration) having a lower percentage of African influence in U.S. demographics today and a list of different reasons for the social changes in the 60s and 70s, I suspect nothing at all would have changed and nothing at all would be different today.
Other than changing the focus of who we
hatedistrust, there would be no substantial change in racial tension in the U.S. had we avoided institutionalized slavery in our history. That one variable is not enough to overwhelm the many other variables contributing to ethnic and racial tensions in this country. This in no way is meant to demean or trivialize the nature of our factual history. We're paying a heavy price for what happened in our history. But that price is due because of deeper problems than the institution of slavery alone can explain. Slavery existed for a reason other than convenience, and it's that underlying reason that's the problem and the reason why basically nothing would be different in the U.S. today had institutionalized slavery not existed here.