I would think it makes some amount of sense if you think they're vegetarian for some moral reason and you think you could court them to become customers.
But why target a market that doesn't want you? Do you really think a burger place can some how override a person's morals to not eat meet? I realize were stretching the analogy here, but what is the point? Maybe if you already saturated the existing market and trying to grow. But then why saddle that market with the wants/needs of the polar opposite?
Given that they come in good faith (trolling is already excepted), I would ask. Burger toppings are predominately plant-based, so perfectly in their wheelhouse. In fact, I'd expect better suggestions from them than the average burger eater.
This seems like a stretch. Another example may be, "If I am throwing a party, should I ask people that I do not invite, what they want?". Sure you could say that they could approximate the wants of the people who _are_ going, but why not just ask the people who are going, directly? It's just noise, otherwise.
> why not just ask the people who are going, directly?
"If I had asked people what they wanted, they would have said faster horses"
You don't poll people to find out what they want. You poll people to gather their ideas. Ideas that you can then leverage to deliver what your intended audience wants, even when they didn't know that they wanted it!
If we assume this party you are throwing has 10 guests, you think you're going to get all the best ideas from those 10 specific people and nothing from the hundreds of people you could have asked? Maybe if you're throwing a party for professional party planners, but otherwise...
In this case I don't see a problem. If you want your opinion to hold weight then put your name/background/credentials/reputation behind it. Not every discussion needs to be fully anonymous and upvote-based.
How would you do it without asking for some applicants' details?