Some argue that the study of history shows patterns by which human culture has developed and is likely to develop in the future. In that sense, veganism and animal liberation may be 'next on the social agenda' - "the next logical step after other inequalities" are corrected. Then a long list of social 'adjustments' is given which, in their scenario, need to come first - or rather, first, second, third, fourth, fifth, etc. It essentially means that, first differences of one's birth condition (gender, geographic and social conditioning, wealth, etc.), then behavioral preferences that are freely chosen (this could become nearly anything the human imaginations can contrive), THEN, at long last, after all 6.8+ billion humans get to poke around and delay the MOST basic justice considerations for nonhumans, we concede that, "OK, nothing left to do but let 'em 'get theirs'."
I have a problem with that selfish mode of thinking, and I'm not even sure it's merely selfish.
To my mode of approaching the collage of persons nature brings forward in natural history, it's just irrational to be "writing a blank check" to everything possible the human imagination can contrive while the MOST basic issues of justice and decency are systematically ignored.
What's MORE 'unequal' (or, if we're relevant, more unFAIR) than abusing and killing animals for food?
I don't see that bears any INHERENT relationship to other social movements that those advocates want to put FIRST (though Peter Singer and lots of others - mostly consequentialists or would-be 'utilitarians' - say "Yeah, go ahead! Put EVERYTHING else ahead of decency with the animals!").
For the animals, what matters is the long wait for decent treatment, not some social claims to entitlements by one subgroup from another.
The things you mention are social agreements among humans.
The first right, I think, is one's right to not be killed or abused. In my way of thinking, that's a bodily claim NOT to be caused to suffer, not a social claim to entitlements.
One can be vegan without adopting animals or giving money on their behalf, but one cannot be an ETHICAL vegan abolitionist and speak FOR abusing them.
One can be a consequentialist and (reluctantly) 'allow' SOME of the abuse if the liberation is on its way, but none of these other social movements seems to do anything EXCEPT DISTRACT the vision from liberating animals from abuse and murder. Ask any of the beneficiaries of these other social movements if they're willing to put aside the arbitrary social behaviors dear to THEM that cost animals their lives - loose and reckless living (vivisection), leather flauting (murder of animals), meat-eating (murder of animals), etc.
That's MY $00.02.
Surely we can start by going vegan at a dietary level and clothing ourselves with decent non-animal attire that didn't enslave and murder a nonhuman person. We can bicker about the doing of medical science and medical research, but toxicology is pretty much ready to replace everything (or nearly everything) we've ever used animals for testing product safety.
As far as Peter Singer's viewpoint: lots of folks could accept that without giving any 'rights' to animals, and that's pretty much how he stars out in Animal Liberation (1975) - not believing in ANY person's rights (as a consequentialist or utilitarian). He sees 'rights' as a social construct that is a tool for helping to make things a little better, progressively, for more and more persons.
But in terms of our 'naive empirical' day-to-day experience, just ask how much real PROGRESS we're making in abolishing the abuse and exploitation of animals.
The numbers of animals used worldwide for exploitative purposes has risen, as have the numbers of animals used worldwide for INDEFENSIBLE exploitative purposes (recreational 'fun food' is NO excuse for murdering someone!).
Making animals stand in line before arbitrary whims and caprices is despicable.
The most basic entitlements to decency should be globally built into every social development program and project, as greening and making safe the energy systems of the planet.
Anything LESS is not truly progressive.