The fear of aliens or strangers is xenophobia. While this usually refers to humans from other countries or cultures, science fiction writers have picked up the term to describe people who are afraid of extraterrestrials.
When we look at how humans deal with people who are different, we can quickly surmise that there will be many, if not a vast majority of, humans who will have problems accepting extraterrestrials. This will probably have a profound impact on how people react after First Contact. If we have trouble just handling the relatively minor differences in human beings, how will we deal with beings that look and act very different from us? The key may be to look for similarities. I think it will be important for us to note the aspects of anatomy, psychology and civilization that we have in common with extraterrestrials. Do they have family units? Do they have a common religion? Do they have festivals and celebrations? How do they handle birth and death? Starting with commonalities will allow us to build a bridge to better understand the differences. Still, there will be many people who will not easily accept human interaction with extraterrestrials and these people might very well be in positions of power. You can imagine there will be a huge debate raging across the planet about how we should handle ongoing contact with an extraterrestrial civilization. It would probably enter into the political realm, as various leaders take sides regarding whether we should be open to extraterrestrial interaction or keep our society closed. This debate will be important and we can only hope that the outcome helps to foster new relationships and does not shut us off from the rest of the universe.
There is a flip side to xenophobia: xenophilia. It is an inordinate attraction to aliens or foreigners with a result that could be detrimental. There will be people who will treat visiting extraterrestrials in a reverential way. It would be easy to make gods out of beings who have the technology to do things we can only imagine. I think this is almost as dangerous as a xenophobic reaction. We must maintain a critical attitude during and after First Contact. It would be a mistake to assume that extraterrestrials are looking out for our best interests. They will have motivations, some of which may be hard for us to understand. They will also have flaws as all biological beings must.
Considering how hard it is for us to overcome racism in our society xenophobia and xenophilia may be issues that will have to be dealt with for many years, and perhaps several generations, after First Contact. We can hope that eventually our world-view will open up to a new larger universal-view, allowing us to find a kinship with other beings.