Great question. I too will assume you only mean extra-terrestrial and not animals.

Here's my take on it:

In most instances we would have no choice. Understand this well: If humanity encounters any extraterrestrial life, it will have found us and not the other way around. Any race that can generate the energy necessary to travel through space could be capable of destruction on a scale humans have never known, and we, boys and girls, are simply half evolved primates who have just recently shot humans into space on chemical powered fire sticks.

In any circumstance that an extraterrestrial is found on earth, and is at the mercy of we Earthicans, we should definitely give it, at the very least, the rights we have deemed for ourselves because those rights are directly linked to our recognition of our own sentience. We understand that we are different from animals and do not behave as they do. An alien may think the same way about us, especially given the current state of humanity as a whole. Probably best not to prove them right.

The existence of aliens changes the game. We would all have to start thinking in a different way. Humans can barely conceive humanity as a whole now without all the barriers that divide us (nationality, language, religion). What will people do if they are confronted with the idea that they are part of a Galactic community?

Since you're referring to alien races and not animals on Earth, it depends. If the alien race comes to Earth in peace, then yes we should treat them equally and accept and embrace them into our cultures. However, if the alien species comes to Earth and intends to hurt us or unintentionally harms us, we should not be so quick to be hospitable. Especially if they choose to attack us, we should attack back.

Actually, we can't even agree on our own rights. Like one country says girls can wear bikinis, others say burkas only. One group of people doesn't want to even hear a curse word, others think the concept of a curse word itself is retarded and on top anyone should be able to listen or watch anything on earth so long as no one is hurt in the making.

But to the trailer specifically,

The "inalienable rights" (no pun intended) that western civilization has agreed to at least in some vague concept stems from an understanding of self, and through that understanding, an understanding of others.

It's argued for instance by at least one vegan on this site that animals should share in these rights. I disagree since it's obvious to me and science they have not reached any kind of level of self awareness, and are completely incapable of reciprocating rights on others much less themselves.

Still though, we treat animals differently based on our percieved level (which is fairly accurate by the way) of their consciousness.

Most have no qualms about squishing a bug, and likely the bug doesn't put much thought into it either. Bigger brained animals are afforded more courtesy than that, most would wreck their car happily to avoid hitting say a dog, myself included, because we feel that on some level they feel. Which it's apparent on some level they do.

But not anything close to our own.

Now it may or may not be the case, that this empathy and self-awareness stems from basically being smart comparatively. According to all evidence we have here on earth, bigger brain = greater self-awareness thus more deserving of rights.

We would have to assume that any being with the brain power to figure out how to travel millions or billions of light years close to, at, or even faster than the speed of light, has a level of self awareness we for the most part would have trouble grasping.

On the one hand, our level of awareness would dictate we would treat these aliens with as much, if not more respect, than we treat eachother.

On the other hand, from the outside looking in, we most likely would not.

And just like I don't blame the tiger for eating Roy, I doubt they would expect much more from us silly and small animals.

Hopefully though I'm wrong.

If they are intelligent beings, with feelings and such, then yes. What makes us the only beings with rights?