When I mentioned that we did not need to triage oppression, I meant as a collective. We do not need to develop a list of what matters most and what matters least. All discrimination is bad.
Also, I agree with you for the most part that people are more important. Thankfully, this does not mean animals don't matter at all, especially when we are talking about the profit margins of a fast-food chain.
I can focus on more than one thing at a time, and most folks do. And, it's quite disingenuous of you to use that article to make a sweeping statement like "people tend to feel more compassion for non-human animals than they do for other people." That study very clearly only about dogs. The authors say that it would be interesting to know empathy responses to other animals (meaning they did not cover it).
It is not wrong to have empathy towards animals.