This is a new term for me so I googled it:
Egalitarianism (derived from the French word égal, meaning equal) is a political doctrine that holds that all people should be treated as equals and have the same political, economic, social, and civil rights. Generally it applies to being held equal under the law and society at large. - wiki
There are two types in my opinion. Notice the "have the same political, economic, social, and civil rights", you can either change the people to match the rights you figured you think are right OR you can change the rights and any laws that violate the rights so that people, as the currently are, are considered equal by that less restrictive set of rights.
Rights can be a great model for creating great societies but they need to be used to model laws and policies and NOT model people (in my opinion) and achieve an Egalitarianism utopia without changing the people but by maximizing freedom using laws that follow a set of rights that are "Egalitarian" with the current society as it is now.
You get the phrase "All men are created equal", yeah naked, dependent, lacking possessions... I don't care to be made equal with babies. Instead look at how people are now in their great variety and find the common things we all share... and make sure laws do not try to change us but just keep others from forcing us to change. This is where a set of rights needs to be thought through very carefully and have the power in the court of law to overturn laws that force us to change or allow some people the power to force some people to change. Laws should have the chief purpose to give freedom by means of restricting those with financial or political power from forcing anybody to do anything beyond their wills. An example is people need to have the right to be poor... you might think "but who wants to be poor?" but I am saying that there are poor people right now who are being forced to work to not be poor, not because they want money but because some laws are out there that people cannot live on the street, cannot live at "no fixed address", etc. I turned off my water and now the city is questioning if it is legal for me to live in a house without running water. They have made up some right that all people have decent housing and the laws then force people to have the housing that they deem to be "decent" by their ideas (not mine). I have to add that there is wisdom in the phrase "All men are created equal" though because when looking for conditions we all share, what you are born with is the minimum you are going to have until you die. Of course the meaning of the phrase goes further back then birth... "created" and "all men" is referring to race being a non-factor with God but I would argue that many other things are a non-factor with both God and nature and need to be a non-factor in the rights and the laws.
When it comes to animal rights, I want to extend that egalitarianism to include both people an animals and then design the rights to reflect what we have now. This makes the rights allowed to be limited in scope as we have food animals and lab experimental animals and genetic patents and other such things that we currently do not allow on humans. If the rights are worded to continue to allow these current practices, then the rights can be enforced and laws challenged that allow people to force animals or people to do things outside of those practices we currently allow. This puts insects and whales on the same page as well as pests and humans. This also applies to what we see in nature like predation. obviously we cannot ban carnivores from killing so we must have the rights limited to allow such natural behaviors.
Of course societies change such as slavery is no longer acceptable so rights need to be adjusted to reflect the current society and the laws need to be adjusted accordingly to fit those current set of rights. Egalitarianism is the key factor I think in changing the opinion on slavery but was accomplished by repealing laws that allowed some people to force other people to do something. Granting freedom rather then banning slavery is the way to go. By granting more and more freedom, I think people's attitudes change for the better but banning things only makes people feel they have become slaves to the laws.
Jan 31 is supposed to be "ban meat" day. I am all in favor of people becoming vegetarian or even vegan (although strict vegans do not have pets which is my objection to a vegan world) but banning anything is repulsive to me. If a cougar can have meat, I should be able to have meat too.