I think it's difficult to change something until you first accept (or at least understand) it. This is probably especially true of situations like this, where people's worldviews are at odds.

What you have to understand is that this person (presumably) really believes that you becoming vegan would be a good thing, and that you remaining a non-vegan is a bad thing. From their perspective, you are both perpetuating cruelty (to animals that they are emotionally invested in the wellbeing of) and damaging the environment (that they, you, and anybody that either of you care about both depend on to survive) through your behavior. Saying to them that they should just respect your choices, then, is insufficient, and doesn't (in my view) give that person or their views sufficient respect.

If you saw a person behaving in a way that you saw as cruel (to people, animals or whatever-it-is that you are emotionally invested in) and damaging to resources that you (and others you care about) depend on, would "just respect my decision" seem a reasonable defense? Maybe you think so, but I'd be surprised if you can't on-some-level relate to someone who didn't.

My advice then would be to forget about "You shouldn't try to change my mind" and focus instead on "You can't change my mind" or perhaps even (if you think it's true) "Your attempts to change my mind make me less likely to do so".

The point is, if you respect this person at all, you owe it to them to at least consider their views.

Now, if you have already shown respect to them and their beliefs (either by listening to their arguments or by researching the subject in your own time) but weren't persuaded, simply explain this. Explain that you aren't sold on their particular arguments for veganism.

It's probably reasonable at this point to concede that there's a possibility an argument or new piece of information may persuade you in the future (it's at least possible, is it not?). Perhaps suggest that they might persuade you better by allowing you thinking space, and that if this thinking space doesn't lead you to veganism, nothing they can do will. Obviously, this depends on what you're comfortable conceding, and how entrenched you feel your views are in the opposite direction.

On the other hand, if you haven't already shown respect to their views, perhaps you can offer to (maybe even on the condition that they stop talking about it afterwards). From your perspective, if feels like they're trying to force you to act a certain way. From their perspective, it's quite possible that feeling you've really listened to and considered their views might be all they were ever asking for.

The only alternative to listening and considering their views, I think, is to simply be rude, and to suggest that what they think doesn't matter, and the consequences they're concerned about are not important to you.

The point is, this person is unlikely to be convinced (short of you successfully persuading them of your views) that it's wrong to persuade you. You have to convince them that their attempts to do so are either futile or actively harmful to their cause.

In the meantime, if they do try to directly influence your behavior (as opposed to your beliefs), explain that you don't believe as they do, and you have to behave in a way that's consistent with your view of things, just as they do with theirs.