Gaius asks whether a liberal who traces her intellectual lineage to J.S. Mill–i.e. who sees the purpose of politics as permitting the widest possible scope for human liberty consistent with the liberty of others–can consistently be in favor of laws for preventing cruelty to animals or protecting the environment:

how [did] liberals, historically, either politically allied themselves with or actually became, some of them, animal welfare advocates, animal rights advocates, conservationists, protectors of endangered species, environmentalists, or nature preservationists, all of whom lend weight to some value or other, different from individual liberty, against human liberty[?]

Historically, I think the answer to Gaius’s question is pretty clear: Mill, and his mentor Jeremy Bentham, were in fact advocates for reform in the treatment of animals. It was largely liberals like Bentham and Mill who brought concern for animal well-being into the mainstream of moral philosophy as well as into the political arena.

Bentham and Mill were utilitarians and justified the arguments on behalf of animals on the grounds that, what counts morally is maximizing pleasure and minimizing pain. Bentham famously said that what matters morally with respect to animals is not whether they can speak or think, but whether they can suffer. Sentient beings are morally considerable because it matters, from their point of view, what happens to them. And while I’m not as familiar with Mill’s thought in this area, it appears, at least from this excerpt, that he followed Bentham in this.

Philosophically, the different branches of the animal rights tradition can be traced to the utilitarianism of Bentham and Mill and to the liberal individualism of Kant (as well as the liberal aspect of Mill’s thought; whether there’s a tension between Mill’s liberalism and his utilitarianism is an interesting question). Peter Singer is the most prominent representative of the utilitarian strain, while Tom Regan represents a Kantian approach.

These two traditions employ somewhat different principles, which sometimes lead to different conclusions. For instance, Singer’s utilitarianism emphasizes the equal consideration of interests, meaning that animal suffering has to be treated the same, morally speaking, as relevantly similar human suffering. However, Singer’s view also allows for killing animals (or disabled humans) if it can be done painlessly while retaining the same amount of overall utility. Regan’s more Kantian position is that animals, as “subjects-of-a-life,” possess basic rights to life, freedom, and well-being and must be treated as ends in themselves. Both positions contend that “speciesism” is an invidious distinction akin to racism or sexism.

Essentially, the animal rights advocate argues that liberal principles–such as equal consideration of interests, rights to life and liberty–ought, logically, to be applied to animals (or at least certain animals). This is usually because it is held that there’s no good reason for drawing the line of moral standing at the species boundary. Thus the animal rights position can properly be thought of as an extension of liberalism rather than a repudiation of it.*
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*The case of the environment may seem trickier, but it might be argued that a liberal could support environmental protections insofar as they are necessary to avoid harm to sentient beings–human or non-human. Liberals and animal rights advocates would, however, disagree with so-called deep ecologists who locate moral value primarily in ecosystems rather than individual sentient creatures.