Rights beyond humans

First, I need to make clear (because so many people don't seem to know this) that the environmental, animal welfare and animal rights movements are three separate things.
Environmentalists are concerned with saving species and even sometimes support the killing of individual animals to further that goal.
Animal welfare groups want to protect animals from neglect and abuse.
Animal rights groups take things farther and want to secure legally recognized rights for animals similar to those for humans.
I would consider myself in support of the first two, but not the third. I believe that in many cases, animal rights groups go too far.
Rather than talk about animal rights, I would prefer to talk about human responsibilities.
Humans are the dominant species on this planet and at least the most sentient one.
No matter whether you believe in the biblical or scientific theory of the origin or humans, you have to believe that we fought for this status.
In the bible dominance is given, but sentience is taken. In scientific theory it is the other way around, but both show humans striving for their present position.
These two states together give us serious responsibilities to/for the other life forms on the planet.
We not only control more of what happens than any other species could ever conceive of, but in fact, we can also conceive of more than any other species.
Unlike the dinosaurs, the last truly dominant creatures, we know what will happen if we run amok and screw things up. This puts the rights of animals way beyond a philosophical question. It is a serious, practical matter.
Being a person with rather strong moral musings, I believe we do have a moral responsibility to prevent and repair any suffering that we can in the world, especially that inflicted by other humans, but I also think it is in our best interest to do so. The loss of species does affect us in countless ways and those are just what we currently know about. We are learning all the time and even though some may think it a drag, I believe it is best to be prudent about what we don't know yet.
And while you may think that there is no practical reason to be concerned with the suffering of a single animal, a story I saw recently about a rescued dog that made a huge difference in the life of an autistic child tells me the opposite.
That being said, I do think it is possible to go too far in our emotional response to animals. For example, with proper regulations, I am not opposed to animals working or food animals being killed. I do believe we should make these animals lives as happy as possible, with comfortable conditions and limits on their work times for example. With proper limits, I don't think it is worse for animals to work than for people to work. And some animals are clearly put on earth to serve as food for other animals, including people, so following the natural food chain is not outside my morality. If someone wants to become a vegetarian, fine, but I don't think it needs to be forced on the rest of us. Personally I think westerners eat too much meat and I oppose eating non-prey animals such as bears, but ultimately, we are omnivores.
IMO, at the present time we are in a strange state in our culture. So much remains to be done to simply protect animals and bring us up to a state of fulfilling our basic responsibilities and at the same time some of us are going off the deep end and exalting animals over people. We live in a country where in some places it is still legal to fight chickens and in other places we are getting ready to eliminate horse drawn carriages. I would hope more people would get concerned about the cruelty that still exists and fewer would be trying to turn animals into demigods.

How much difference would it make?

A few words on the divide between left and right.
While I agree that it would improve the general atmosphere in our country if we both stopped demonizing each other and tried to see each other's point of view, I don't believe it would make the difference some think it would.
It's true that some of the negative attitudes come from leaders and media types that profit from them with more votes, viewers or whatever. But they have to have something to work with at the beginning. If anyone thinks that things would be peaceful and harmonious without these incitements, they are just wrong.
It would probably help all of us to know how the other side sees their positions and themselves, but that would not make us agree with their view. If we were going to agree with their viewpoint, we would have done it already.
Conservatives who get to know gays or women who have had abortions as basically nice people will most likely still see them as sinners condemned to eternal hell in the afterlife.
Liberals who get to know right to lifers or klan members and see that they treat their families well and give to charity will still see them as intolerant and cruel, if not downright dangerous.
One thing I believe is a fundamental tenet of liberalism is that there needs to be a place in the world for most people, even people who don't fit the mainstream, or those we disagree with. There are limits of course, but as much as we can we try to allow a place for all types. So we would certainly agree that there is a place for the right wing somewhere in the world.
That doesn't mean the place has to be in our face.
And if we who support diversity still want some freedom from it in our lives, what can we expect from the side that supports narrower straits?
Being respectful to each other is certainly a good idea, but it won't end the deep philosophical battle.