As I hope we're all aware, there was (and is!) a great deal of pseudoscience utilized in service of white supremacist narratives. This kind of thought experienced a flourishing in the United States in particular during the 19th century due in large part to the growing controversy over chattel slavery. Many modern racist ideas draw their framework and reasoning from ideas popularized at this time.
I was thinking about the slave-owner Calvin Candie from Django Unchained. A large and interesting part of his character deals with how he clings to racist pseudoscience in order to justify his atrocities to himself. He considers himself an intelligent and sophisticated man, and so requires a fig leaf of pseudoscientific legitimacy to lull his atrophied conscience to sleep.
Of course it was all ludicrous and not based on actual observable facts. Which begs the question: where did it all come from? Where did the men Candie is based on get all of this racist psuedoscientific information from? Were there think tanks generating this kind of stuff? Did people actually hold massively slanted experiments to try to prove racist ideology true? Were there prominent figures producing a lot of work in this field? Were archaeological findings twisted to fit the racist narrative? Where and how did they manufacture this erroneous proof?
Much more can be said, but consider:
How did phrenology survive as long as it did? written by u/CopperBrook which covers one type of pseudoscience from a British perspective.
A bit of discussion on the scientific community in your time period What are some of the more notable (scientific) critiques of scientific racism - especially in the 19th century? written by u/restricteddata
As for how a non scientist would have access to scientific racism, the first paragraph discusses a popular book on the topic: In The Great Gatsby, Tom reads white supremacist books and goes off on a racist tirade against interracial marriage. Nowadays we see this as proof he's a scumbag, but what would Fitzgerald's original audience have thought of it? written by u/hannahstohelit
You might be interested in my answer here.
To summarize the key takeaway, natural historians didn't claim to have "discovered" racial difference; rather, the construction of racial categories began much earlier, in the political sphere. The earliest works of modern taxonomy (e.g. Linnaeus) already took these categories for granted. Physical anthropologists (e.g. Blumenbach) tried to identify "scientific" ways in which these self-evident categories might be delieanted. This was never a movement or school of thought; it was just part of regular science like everything else. Candie could have picked up most any book and found something with which to justify his views.