So there are several ways one could answer this, depending on how one defines "race science," "scientific racism," "disputed," and "disproved." Scientific racism is not really a single "theory" that can be proven or disproven; it is more like a framework through which some people see and analyze the world. The result is that the changing views of the scientific community around race (which are hardly static even today) are less the result of any concerted or specific work, but rather the emergence of alternative understandings that are just not that compatible with these other views. So there isn't some kind of simple answer here. You are asking about a process of scientific change that took the better part of a century to happen, was also closely connected to various kinds of social changes that were happening at the time (including the examples of the Nazis, the Holocaust, the Civil Rights Movement, and so on).

But if you are looking for one example of how some of this worked, one standard example is Franz Boas and the Boasians. Boas was a physical anthropologist at Columbia University in the early 20th century, and he greatly resented the racist theories of human populations, and eugenics in particular, which were popular among certain circles in the northeast at the time, notably embodied in Madison Grant, the New York lawyer/philanthropist/natural historian who was deeply connected in New York society, the Museum of Natural History, and so on. Grant was the creator and major proponent of Nordicism, which was essentially an early version of the same race theory that Hitler would later adopt (and rebrand as Aryanism). His writings were deeply anti-Semitic, anti-Eastern European, anti-Irish, anti-immigrant, anti-Black, and in favor of coercive eugenic policies ranging from sterilization to essentially extermination.

Boas loathed Grant (and Grant loathed the Jewish Boas), and did a lot of work in the 1920s to undermine Grant and the kind of people who liked Grant. Some of this was scientific research and argumentation, usually along the lines that supposed biological racial differences were mostly matters of culture and environment. One of the major pieces of "data" that the eugenicists of the time liked to bring out to talk about racial differences was the Cephalic index, which is just the ratio between the width and breadth of the skull. The scientific racists and eugenicists would note that new immigrants from Eastern Europe had much different Cephalic indexes than people who had grown up in the United States, and used this to argue that despite their apparent whiteness, they must be quite different in their mental power and abilities. (Nordicism is a "divide up the whites" form of racial categorization — it put most of its emphasis on identify "bad" European races, like the Irish, the Slavs, the Ashkenazi Jews, etc., as opposed to later "black and white" racial theories that became more prominent in later decades.) Boas showed that, actually, the Cephalic index was pretty determined by the environment: the children of immigrants who were born in the United States, had the same Cephalic index as other "native born."

That sort of thing is nice and important, but as you can imagine, people who are committed to a racist viewpoint are not going to be swayed by such a thing; there are a million reasons that people can (rightly and wrongly) ignore or throw out or reinterpret data that doesn't fit their worldview.

What Boas did that was perhaps more impactful in the long run was train a lot of good students and work very hard to maneuver them into positions of power within the discipline of anthropology. Some of his students are still pretty famous today, like Alfred Kroeber, Ruth Benedict, Zora Neale Hurston, and (the most successful) Margaret Mead. Boas and his students essentially took over the academic instruments of anthropology in the United States, and then used them to exclude the eugenicists and their points of view from respected anthropological journals, textbooks, academic conferences, research funding, and so on. The Madison Grant types didn't just shrink away, of course, but they became more isolated, had to create their own eugenist-societies, and got further and further from academic respectability. And so in a generation or so, if you wanted to learn more about human cultures in a university, you probably were going to learn something more like Boas than like Grant. This should not be taken as some kind of magical overthrow — it wasn't — but these kinds of things do amplify some positions while dampening and isolating others.

When Hitler came to power, Boas was keen to use the engines of publicity to a) show that Hitler's racial theory was considered very out of date by "true scientists" (read: him and his students), b) show that Hitler's "scientific racism" was really just a justification for his political policies (not "real science"), and c) associate these kinds of awful beliefs with the Nazis (who, as time went on, became exactly the kind of people you didn't want your ideas associated with). So in his own perverse and inadvertent way, Hitler was perfect for the plans of Boas and his students, because the association let them even further their agenda of being the "real" scientists.

When World War II ended, one of the goals of the new United Nations was to prevent the kinds of atrocities that the Germans had enacted from occurring again. Among the many approaches to this end, the United Nations Educational, Scientific and Cultural Organization (UNESCO) was created. Boasian-style scientists were able to gain control of the biology and anthropology aspects of UNESCO, and used it to further push an anti-racist agenda. In 1950, they issued the controversial Statement on Race, and several follow up "statements." I don't want to get in the weeds as to the contents of the different "statements," but the goal here was to essentially try and come up with an official line on "The Race Question," as it was called, and its relevance to science. The various statements varied a bit in what they said race was or wasn't, but the essential argument in all of them was that racism had no scientific basis. Not all scientists in the world, or even in UNESCO, completely agreed with this sentiment, to be sure! But I bring this up as another conscious attempt by some scientists (the most famous here is Ashley Montagu) to use essentially social and political instruments to create a context for certain kinds of scientific theories, deliberately relegating what they considered scientific racism into an area of non-science (politics). (If you think it is ironic that they would use politics to do so... these things are complicated. Both sides of this issue saw their "scientific" work inextricably connected with political implications, and both used "politics," broadly speaking, as way of pushing their particular agendas. Historians of science largely reject the idea that politics and science are as separated as our tropes around the purity of science would like them to be in an idealized world, and that is not only true of the "bad science.")

Anyway — I am just offering up this particular example as part of the story. There is no "real answer" to this question, because many of these things have not been in any way "conclusively disproved." It is more that most scientists do not regard some of these theories/frameworks as being within the domain of scientific inquiry, and do not regard them as being "interesting" questions anyway. That is its own line of discussion about how scientific communities drop theories/frameworks even if they don't have some crucial data or experiment justifying it (the idea that science works by "crucial experiments" that determine what they believe or don't is not quite right most of the time, and certainly not in areas as nebulous and broad as human differences). A large part of the drift from racist theories in science has not been because of some specific piece of data or argument, but because the kinds of people who were doing this science tended not to be the kinds of people who really thought that racism was a subject worth of scientific study. Some of that is due to deliberate institutional changes made over the years by scientists and others, as well as differences that occurred in society over these decades (there are still over, old-school racists and there are still anti-Semites and so on, but they tend not to get PhDs in Anthropology and land university jobs and become prominent — at least, not in the way they could in the 1920s).

A really great paper on the Boasians and their work is Jonathan Spiro, "Nordic vs. anti-Nordic: the Galton Society and the American Anthropological Association," Patterns of Prejudice 36, no. 1 (2002).