During the Lincoln-Douglas debates, the case for "bracketing a controversial moral question (i.e., slavery) for the sake of political agreement," according to political philosopher Michael J. Sandel, was made by Stephen Douglas.
Sandel argues that whatever his personal moral views, Douglas claimed that, for political purposes at least, he was agnostic on the question of slavery; he did not care whether slavery was "voted up or voted down." Lincoln's reply was monumental in its moral significance:
It is only reasonable, Lincoln argued, to bracket the question of the morality of slavery on the assumption that it was not the moral evil he regarded it to be. Any man can advocate political neutrality, Lincoln continued, "who does not see a wrong in it; because no man can logically say he doesn't care whether a [moral] wrong is voted up or voted down."
Douglas's political conception of justice (e.g., neutrality on difficult moral questions) depended for its plausibility, as Sandel writes, on a particular answer to the substantive moral question it sought to bracket (i.e., slavery). Lincoln rejected Douglas's answer to this moral question, instead arguing that political (or moral) neutrality on the issue of slavery, even for the sake of the Union, was morally reprehensible.
Those who believe that the issue of animal exploitation is a substantive moral question, similar in kind to that of slavery, sexism, economic injustice, genocide, etc. argue that as the abolitionists of the past threatened the very stability of the Union by their beliefs and actions, they are willing to do things considered improper or impolite, lacking in tact, overly aggressive - things that indeed may challenge the very stability of their personal relationships, social status, or job opportunities. Indeed, in a perfect world all organizations that profit from the torture of animals would be relics of the past (would this include P.E.T.A.?), like the plantations of the South.
For example, when I broach the question of the rights of animals in my conversations with others, the most frequent reply is Libertarian in nature: "You (Alex) live your life as you wish, I respect that, and I will live my life as I wish and you should respect that as well - be neutral and I will too." Or "You have no right to force your beliefs on me." If the issue is rightfully pressed, hostility is common.
Consider the assumption being made in both responses. Quoting Lincoln, in part: "It is only reasonable...to bracket the question of the morality of [animal exploitation] on the assumption that it is not the moral evil that it is." [emphasis added]
To advocate neutrality in response to my questioning the morality of eating meat, for example, assumes that my negative answer to the substantive moral question of "Is the exploitation of animals moral?", is wrong and that the non-vegan's positive answer is correct or more plausible. As Lincoln argued, "Any man can advocate political neutrality...who does not see a wrong in it." You are positing a belief, and one cannot simply assume the soundness of that belief. Critical analysis is a necessary requirement to move from the realm of prejudice or "tradition" to a position grounded in reason and logic.
As Lincoln could not logically (or morally) bracket the substantive moral issue of slavery for the sake of political agreement, nor can I logically bracket the substantive moral issue of how individuals relate to nonhumans for the sake of agreement, or peace in my relationships with others.
Considered another way, John Stuart Mill's 'Harm Principle' has been succinctly articulated with this simple maxim: "Your right to swing your fist stops where my face begins." I believe this maxim appeals to a moral truth that is applicable in our dealings with nonhumans.
If you eat an animal your behavior is what Mill called other regarding: to do what you want to do necessarily requires the invasion of another individuals physical integrity in a most fundamental way (e.g., an animal's life is taken for your consumption). These actions cannot be explained away by an appeal to neutrality: you are harming another individual, which requires a justification. The right to have your desires satisfied, if it necessarily involves "other regarding" behavior, ends where the basic rights of other individuals begin.
One cannot bracket the substantive moral issue of "other regarding" behavior for the sake of dispute resolution, nor can I logically (or morally) say that I don't care if it's "voted up or down," metaphorically speaking.
Lincoln once said, "I am in favor of animal rights as well as human rights. That is the way of a whole human being." I couldn't agree more.