It is probable that the right specifically use the word 'alien' to refer to people without an appropriate visa or citizenship to invoke feelings of fear in the population, but why is the concept of alien so frightening?
I would put it down to the idea that the word alien is most commonly applied to extraterrestrial beings who supposedly abduct people in the middle of the night to perform awful experiments on them.
But our vision of aliens have changed over the years, where aliens have mostly been aggressive seeking to invade and take our planet, and sometimes their aggressive nature has manifest in our technologies, like with the X-files, a common thread was that aliens presented as black oil.
Aliens have pretty much presented themselves as aggressive or something to be feared with two notable exceptions, Star Trek, especially the original series, which was very much emblematic of the 60s; the other except was Kubrik's 2001 where aliens are a kind of beneficial force, and the movie Contact - where aliens serve as a kind of mirror for humanity.
And I think this is the purpose that aliens really serve for us, they are a metaphor for our hopes and dreams, our fears and technology.
Regarding our technology, earlier this year there was a rash of articles saying aliens might attempt to communicate with us via DNA, which has advanced our understanding in a number of ways. I still think we have much to learn about DNA, things like that it is a kind of hologram that must be read across a number of chromosomes at once, not just down the lengths of chromosomes, one at a time like when it is being reproduced.
I think our fear of aliens is based on our fear that aliens will be just like us - or attitudes when we colonized landmasses like Australia, the Americas, the islands in the pacific and else where. Western arrogance had no respect for the natives of these lands and introduced western diseases, claimed and destroyed their lands, ruined the native people's culture, traditions and harmony with the land.
We are afraid aliens will be just like us, coming with their superior technology and then wipe our culture out.
I suspect when we meet aliens they will be nothing like us and would rather be more afraid of us.