Evolution should already ensure that species will not want to mate with other species often. This is due to a principle of Koinophilia. On the most basic level The odds of a hybrid species being healthier then non-hybrid is unlikely and thus we all have an instinctual aversion to mating with someone from another species because it's likely our children would be less fit then if we had a child with someone of the same species.
Actually avoiding mating with another species is a specific example of a more general principle. We will instinctual avoid mating with anyone that looks abnormal compared to the average for our species, it just happens another species usually looks pretty abnormal compared to our own. People that look substantially different usually had mutations and, despite mutations being mandatory for evolution, most mutations were detrimental. Thus we institutionally learned to avoid anyone that looks significantly different from the norm because the odds are they have a mutation that would harm any child we had with them. This effect is a major part of how distinct species came about a all!
The lack of more numerous hybrid sub-species in present day, or in the fossil records, is often refereed to as Darwin's Dilemma, he couldn't figure out why individual species existed at all, he would have expected a whole gambit of intermediate stages between species to exist due to multiple levels of hybridization. He listed this confusion, that distinct species came about when it was possible for species to interbreed, as a potential argument against his evolutionary theory in fact, it wasn't until a little later the Koinophillia was recognized as the cause for distinct species. Once two groups of animals looked distinct enough they would avoid mating with each other, allowing them to evolve and diverge further over time into clearly distinct and separate species.
The point being that preventing hybrids from diluting your prue-bred genepool isn't much of a problem, evolution would have already instilled instincts that prevent this, if it hadn't you wouldn't have distinct species. After all when's the last time you heard anyone say they thought that chimp was HOT? If tomorrow all great apes were able to produce hybrids with humans, and the hybrids were healthy & sapient, would you be attracted to a gorilla? I think the thought of producing a child with an ape would feel wrong, even revolting, to many people, that is koinophillia, and it's how your species would feel about inter species relationships as well.
The harder part to justify is actual the presence of a non-trivial number of hybrids in your world despite the evolutionary instincts to avoid this. Still, this may not be a big problem, humans focus on thinking/learning has resulted in less focus on instincts and thus it's a bit more excusable that humanoids violate the usual koinophillia instinct then many other species are prone to. Plus, it may be that hybrids set off the "koinophillia' radar even more then each distinct species, making the hybrid struggle to find mates even if produced. Basically a degree of hybridization which is low enough will still be sustainable, particularly if hybrid species rarely find people interested in having children with them.
I should stress, this koinophillia does not require overt racism or hatred between the species. koinophilia is purely instinctual affect on mate choice, not view on species as a whole, and even the most open minded of humans still show signs of instinctual Koinophillia! It doesn't require one to believe one species is somehow less important then them, or to believe that a species or hybrid species is wrong. However, one may simply happen to find one women attractive, on an instinctual level, and another not attractive; just as someone may be attracted to blond hair over red in women (in fact, koinophilia almost certainly plays a role in hair color preference....)
From a story perspective imagine someone saying "she is nice and all, but I just can't deal with scales" or "The gnomes are so small, Id feel like I'm dating a child" or "I just prefer red heads, not tentical hair". basically the overt physical differences will feel 'off' to a different species and unattractive to most people, without their recognizing the cause is koinophilia. They may still respect and get along well with another species, just as someone may love their dog or a zoo warden may grow to respect apes in their care, they just won't find them attractive on a sexual or romantic level as often.