Veganism is most often associated with the left. This isn't an inaccurate generality, stereotype or prejudice. Most often, a vegan is someone on the left side of the false two-party illusion.
However, that does not mean every vegan is on the left. Some people who advocate for veganism and identify as vegan are also politically aligned towards the right. Some are even towards the center.
In all of these cases though, the commonality between any political alignment is that they all support the ideology of government and external authority to impose the decisions that a centralized group of people decide upon the majority.
Thankfully, there are some vegans who are opposed to government, to the state, to statism. These vegans are anti-statists. By being an antistatist, it usually means that they are supporters of anarchism.
And by anarchism, this refers to the etymological root of being for no rulers, or to say it another way is no masters and no slaves. Because otherwise, to accept the legitimacy of authority in government, is to also accept and support the idea of rulers, or masters over our lives and thus making those who are not making the decisions and imposing them on others relegated to the position of slaves of some form.
That isn't to say they are outright slaves in bondage, in chains, living on an explicit plantation that is easily visible to distinguish it as such. But it is a form of enslavement due to the monopoly on violence for disobeying what the rulers say you must do.
A restriction on your freedom to choose, on your free will choice, as long as your choice does not involve harming another, is an imposition of a form of control and therefore enslavement of some degree.
There are nuances to this, but essentially that's what the core of the philosophy entails when you are anti-statists or not and are pro-government instead.