I agree that the origins of the anthro race would have a large influence on how modern-day humans would accept them. If anthros preceded humans, it is possible that anthros would be seen as the superior race. If anthros came after the evolution of humans, or if anthros existed in isolation until "discovered" by the human race, then they would likely be seen by humans as inferior.
As for racism and cultural tensions, the whole of human history is fraught with violence and judgement against those whom are deemed different, and that's just within our own species. Of course, humans are also capable of great compassion and great deeds. So the human race itself is divided between acceptance and segregation...and even when it comes to human views on feral animals, people run the gamut from "who cares about an animal life, let's skin it!" to people who spend their entire lives attempting to protect animals from physical and environmental harm.
So that being said, I think it's extremely likely that anthros would be subjected to human discrimination if humans considered themselves the dominant race.
On the flipside, we have to ask ourselves just how "human" our anthros are. Are they susceptible to the same feelings of racism or speciesism? Do they feel emotions the same way humans do? Do we consider all anthros to be more emotionally stable and benevolent than the human race as a whole...as in an enlightened race, perhaps?
Or are they just as flawed as we are? Could it be possible that anthros themselves would have as much infighting as humans do? I think the "human" aspect of our anthros makes them very much like us, just with different physical features than humans. And just as humans are capable of coexistence or war, so too I believe anthros would be.
Which means of course that human-anthro interaction would likely run the gamut from intermarriage to full out war, depending on what conditions are existing in the world. There would be oppression of anthros by humans, but perhaps anthros could also oppress humans. That's the unfortunate aspect of being, at least partially, human. Of course, the human side also brings with it incredible capacity for logic, reason, and emotion. So it's all highly subjective to environmental factors, if you ask me.
On the other hand, we also have to measure just how "feral" our anthros are. Do they follow a pack structure or tribal structure? Do they respond to danger or agression in animalistic or in human ways? How would laws governing human aggression be adapted for an anthro race? Would the animal side of them make them more or less likely to behave aggressively?
Personally, I have a difficult time when I come across imagery of anthro fascists, for example. It's difficult and uncomfortable to consider that our beloved anthros could be capable of the same evil that humans have been capable of in the past. Personally, I'd like to believe that they'd be a bit more in tune with nature and a bit more evolved emotionally and mentally, so as to be good stewards of our planet and of each other. But that's an idealistic view. The reality is that anthros would be just as diverse as people, and likely prone to similar social conflicts as any other race of human that was deemed "different" in the past.