It's all word views. Obviously a Christain who believes in souls has no reason to respect an animal if it doesn't have one.
But, I just think we are matter, so I imagine that matter inherently experiences. In that case, humans are no longer the obvious protagonist who has no reason to feel bad about abusing the rest of those out there.
Edit: And the fact that racism likely comes from people looking different, acting different, having resources we want, difficulties in communication, and/or leaders having an incentive to support it, it is pretty easy to see how specism exists. Whethere or not you care about that is up to you.
I think the word anarchy is bad branding. (Though good branding is impossible when the king want his citizens to hate you.)
From what I understand, the main goal of anarchy is to remove the system that separates us from power. For example, representative democracy makes it so you just go "pretty please represent me" without having any direct agency over the world around you.
Anarchy is not "remove all the rules".
Edit: if there is a system that facilitates personal rights and agency then it is not necessarily against anarchy.