I think that in a world where a lot of people can be quite racist, sexist, intolerant of different religions and homophobic against their own species to varying degrees due to superficial differences to even the point of extreme violence, despite having thousands of years to get used to each other, a completely new and difference species we barely know just suddenly appearing would have the same affect but worse. Depending on how different they look, act and believe from us, the more we will be afraid of them and hate them - even if they come in peace - and even the most open-minded people would have issues talking and being around something so new and different, despite their best efforts.
It won't be us discovering them, but them discovering us. And likely they will be indiscriminately racist against all humans. Maybe not at first, but give them time to observe our behavior as a species. Unless they're just as bad as we are, or worse. Then it won't matter how racist humans are.
While the scientific community has gone back and forth on whether it's likely that life exists in the universe outside ourselves (arguments "for" being the unlikeliness that our habitat is 100% unique in the world, and "against" being that any intelligent and highly developed species would have already destroyed us), if it is the case that there is intelligent life outside of ourselves, those most likely to resent this, be fearful of it, or express frustration or anger are those who believe strongly that we are the only ones out here - namely, the religious. It would be very likely that those people who have dedicated their lives to a scripture saying that a deity hand-crafted us in his image, in the void of space, to be unique, would find the fact that their belief system is a farce a hard pill to swallow. The mere existence of other life in the universe would turn their faith on its head, and would draw scorn if not outright hate from some. I won't go so far as to say all, as some religious people would find a way to integrate the reality of the situation into their belief system. But that's some, not all.
Most people would be very happy about the aliens, since the aliens would probably come bearing gifts of new technology and our entrance into interstellar trade and commerce. I would love the opportunity to meet aliens, have relationships, and ultimately marry an alien. That would just be phenomenal. Earth is boring. I want to go to space.
If we were to discover a new species of intelligent alien life, and people instantly developed a hostile attitude toward each of them based simply on the fact that they are aliens, that would not be racism. Racism has to do with negative attitudes about human beings of a particular race.