There was a tremendous amount of "dehumanizing" racist propaganda about the Japanese directed at the American public during World War II, as part of the US government's efforts to maintain American enthusiasm for waging war, to encourage investment in things like war bonds to finance the war, and to discourage people from having too much sympathy for what happened to the Japanese both abroad and domestically. It was also, it should be said, fairly "self-generated" as well — the government did encourage these sentiments, but many of the anti-Japanese sentiments were legitimately and indigenously held, as a reaction to the Pearl Harbor attack, and 1940s United States was an inherently racist culture in the sense that racist attitudes were normalized and structurally enacted (and not just in the South, which was still segregated and under Jim Crow). This does not mean, of course, that every individual felt the same way towards the Japanese, or that things like the firebombings and atomic bombings were universally popular, but it was part of the overall context and mostly taken for granted. Editorial cartoonists for major US newspapers, for example, could easily present racist caricatures of the Japanese and not expect criticism or protest; this is quite a sign that these attitudes were just seen as part of the landscape of the times. (This sort of thing, by the 1940s, would no longer have been acceptable in the case of Jews or, in the north, African-Americans. That doesn't meant that anti-Semitism or anti-Black racism were not both prevalent in these places, but there is a difference between when these things are allowed to be explicitly voiced in the public sphere, and when they are either "base motivations" for activities/policies, or considered some kind of taboo sentiment not meant to be voiced.)

It is hard to measure the "impact" of racist attitudes on public opinion on anything, much less the atomic bombings. It is not as if one can easily have people check a box as to whether they are racist or not, and then do a comparison of how their views on other topics change as a result. One could imagine clever studies that would, in some other way, try to discern what kinds of racist attitudes a person subscribes to, and then see how that correlates with other opinions they have. But no such studies were done in the 1940s (in part because, again, the racism of some form was mostly taken for granted, but also because public opinion polling was still in its infancy and the methodologies were pretty loose by modern standards). Racism (as I've elaborated on a bit in an answer different but related question is not just a "variable" that gets switched on or off in an individual person; it is a complicated social and psychological phenomenon that is extremely pervasive and affects a huge number of thoughts and interactions without most people even being consciously aware of it unless it is explicitly pointed out (and even then, they tend to try to rationalize it). So measuring its "impact" on opinions is pretty tough.

One can say, that US public opinion was by and large pretty unsympathetic to the Japanese, and one can say that part of that is probably related to dehumanizing propaganda. Polls from 1945 indicate that the vast majority of Americans supported the use of the bombings (one from October 1945 put it at 85% in favor of their use, only 10% not; interestingly, in this particular study, 90% of people with a college education approved, 86% with only high school, and 83% with only grade school). Another poll from December 1945 diced it up a bit more: only 4.5% thought the bombs shouldn't have been used at all, 13.8% thought that some kind of demonstration (e.g. using the bomb on an unpopulated region first) should have been done, 53.5% thought it should have been done exactly as was done, and 22.7% remarkably agreed that "we should have quickly used many more of them before Japan had a chance to surrender." (Any missing percentage points in the above are people of no opinion.)

So the numbers vary depending on the question and time asked and probably the specific audiences of the pollsters (again, the methodology for opinion polling back then was pretty dodgy by modern standards, so we can't put too much stock on these), but I do think that it is remarkable that 1/5th of the Americans in that last poll were unhappy with the bombings because they wished there had been more of them is a remarkable statistic and grimly indicative of the antipathy towards the Japanese. I am sure that very few of those people would had justified it by saying that they believed that the Japanese were subhuman; most would likely have said that they thought the Japanese "deserved" it because of Pearl Harbor, their atrocities, their war crimes, etc. But that is still the kind of place where racism tends to come in, even if not as the overt justification: it adds intensity to negative feelings, it decreases empathy (in this case, with civilians who had no ability to impact the conduct of the Japanese military and government), and it encourages even people who might not be that inclined towards violence to look the other way and not make a fuss. But again, it is not some simple "variable" we can toggle on and off in some easy way, and is just part of the overall mix of how people at the time would have regarded the Japanese, as well as how they regarded the targeting of civilians more generally during a war that involved quite a lot of that on all sides. But it would be quite bizarre to somehow not expect that it didn't play a big role in public opinion, given that was part of the overall context in a very explicit way.