Are Veg*ans Oppressed?
I've long agreed with nosnowhere's side -- I think it doesn't make sense to think of ethical veg*ans as an oppressed class. To explain why, I look to the contrasting aims of tolerance versus universalization, and an analogy with feminism. To be oppressed is basically to be treated as if you or your activities are less valuable, and to suffer added costs and harms, on the basis of some characteristic. By this standard, women constitute an oppressed group in our society -- in a variety of ways, women and feminine activities are treated as less valuable than men and masculine activities, and women face higher hurdles in their lives. When someone recognizes oppression, their desire is for what I'll call "tolerance" (admittedly a word troublesome history). Tolerance means that people oppressed on the basis of a certain characteristic want to be able to live their lives free of the oppression that disadvantages them relative to people without that characteristic.
When enough people recognize a form of oppression, they can form a movement with its own name -- in the case of oppression of women, "feminism"*. The goal of a feminist with respect to women is to end the oppression and achieve the above-mentioned tolerance. But the goal of feminism with respect to feminists is not tolerance but universalization. Feminists don't want society to tolerate feminism, allowing feminists to do their feminist thing on an equal basis with anti-feminists. They want to win, converting everyone to their views about the existence and badness of oppression of women -- aiming at tolerance of feminism undercuts its ability to achieve tolerance of women.
Feminists do face hardships for being feminists, over and above the hardships they may experience as members of the movement's intended beneficiary class (i.e. women) -- for example, being stereotyped as unattractive and humorless, and having their views discounted as coming from an irrational fringe. But these hardships take on a different meaning because of the different status and desired end goal of feminism versus womanhood. Since feminism is a movement aimed at changing the prevailing social system, it is unsurprising that the system would -- passively or actively -- throw up obstacles. So while it's entirely reasonable to work to reduce those obstacles so as to enable feminism to achieve its goals more easily, there is a real difference between the first-order oppression perpetrated by a social system and its derivative resistance to people who challenge the first-order oppression.
The analogy here, I'm sure you've figured out, is that animals are like women in being first-order oppressed, and veg*anism is like feminism in being a universalizing movement encountering resistance in its quest for tolerance of the first-order oppressed group. To call veg*ans oppressed, then, is to conflate two different sorts of relationship to an oppressive social system. (Though the situation is muddied by the fact that even many ethical veg*ans adopt a posture of seeking only tolerance for veg*anism as a way of avoiding unproductive conflict with omnivores.)
The hitch, though, is that this analysis applies only to "ethical veg*ans" -- people who take up veg*anism as a way of advocating for the interests of animals. But there are other reasons to be a veg*an -- because it's cool, as a personal spiritual practice, because you think it's healthier, because you hate the taste of or are allergic to animal products, etc. Such "non-ethical" veg*ans adopt the same diet as ethical veg*ans, but because their aims are not built on achieving tolerance for animals, they can consistently advocate for tolerance, rather than universalization, of veg*ans. And because of that, I think non-ethical veg*ans -- who face the same hardships qua veg*an as ethical veg*ans -- can lay a claim to being victims of a first-order oppression (in somewhat the same way that a lack of accommodation for kosher diets is an aspect of first-order anti-Semitism**).
*For convenience, I'm using "feminism" in the very broad sense that covers anyone opposed to women's oppression, though I recognize that some people dislike that term because they see it as referring to a specific and problematic diagnosis and program for action.
**I found this post interesting because an Orthodox Jewish friend once told me -- and I don't know how widely this theory is held -- that the whole point of the kosher laws is that non-Jewish society will be unlikely to tolerate people who practice them, thus encouraging Jews to maintain a close-knit autonomous community rather than blending in with their neighbors. And while I'm tangenting, I also wonder whether, given that AFAIK all vegan food is kosher, an attempt to tolerate both Jews and vegans with the same meal would actually fail to fully tolerate Jews because it would impose added dietary restrictions (e.g. "if you don't want to be forced to eat a cheeseburger, you have to give up hamburgers too").