I'm a strong believer that it's a mistake to appropriate the experience or struggle of any oppressed group or individual to further our own cause, especially if our advocacy is not designed specifically to address their exploitation. As such, I believe it is inappropriate when we use how other groups are the targets of oppression to describe being vegan or to use their struggles against oppression as a metaphor for the vegan movement. I say this for the simple reason that vegans as a group are not ourselves the targets of oppression.
Complaints that vegans are an oppressed group come fairly often. Usually the complaints come from privileged individuals, such as well-to-do Whites, particularly men, who might make the claim that veganism is their struggle. (For instance, one affluent White male has claimed something as absurd as his inability to buy a veg version of the burritos at an upscale fast-food restaurant that exploits other animals is a form of "oppression.")
The fact is, veganism just isn't like most movements for social change, which are rooted in the oppressed group's collective struggle against the system that oppresses them. While the vegan movement can only remain relevant as long as it broadly opposes all oppression, it is the oppression of nonhuman animals that veganism specifically seeks to center and eliminate. That is, veganism is a movement where we occupy the privileged position of human under the very system of human supremacy that we seek to abolish.
As humans, our position in relation to other animals is closer to that of men over women, Whites over people of color, cissexuals over transsexuals, citizens over non-citizens, abled over disabled, straight over LGBQQ, and so on. In each case, the former is in the social and political position to benefit from how the latter is the target of oppression. In fact, no action is required on the part of the former to benefit from the exploitation of the latter. These benefits come from the inequities that are built into a structure of society.
In this respect, veganism is an ally movement. It has more in common with male anti-sexist allies, White anti-racist allies and so on, than it does with the struggle of women against sexism or Blacks against racism, for instance. Vegans, like feminist men and anti-racist Whites, will inevitably have to give up some privileges afforded to us with respect to our privileged social status as humans when we make a commitment to being anti-speciesist allies. This does not mean that we are the targets of oppression anymore than men are the targets of sexism or Whites are the targets of racism.
When a White person, for example, is criticized by another White person for doing something as simple as acknowledging that racism exists, the ally is not experiencing racial oppression. They are witnessing the other person's backlash and denial. Being an ally may cost them some friendships or even a job, but it does not fundamentally alter the fact that the person moves through the world with all of the privileges of a White person, which includes the countless unseen benefits that accrue to White people at the expense of people of color. Moreover, the ability to avoid racist people is a privilege in and of itself.
Similarly, the inability of vegans to find animal-free products with the same ease with which one can find animal products does not make vegans "oppressed." It takes conscious effort to be an ally. One must necessarily go out of one's way in order to avoid participating in oppressions; that is how oppression works. Being thought of as odd or making people uncomfortable in social situations because they do not know what to feed you also does not constitute oppression. Those things are the result of standing up against the oppression of other animals, which will necessarily make people uncomfortable because something that is normally silenced and unquestioned is being called into question.
This is not to say that people who are vegan can't also be a member of a group targeted by oppression. If we are the target of sexism, racism, cissexism, xenophobic-nationalism, ableism, heterosexism, and/or some other form of oppression, then we are going to still be the target of these forms of oppression even as a vegan. But, again, this is not specifically because we're vegan.
The barriers and opposition that we experience as vegans are meant to hold the structure of human supremacy in place, not oppress us as a group of humans. So while anti-veganism is a real and persistent occurrence, it's important to remember that nonhuman animals are the true targets of this backlash, not us humans. So there is no appropriate metaphor in this regard for placing vegans in the position of an oppressed class of people.