That’s not how that works, the problem of getting marginalized people ID cards isn’t solvable by someone in food service. The problem of selling food to your customers in a manner that doesn’t require government ID is.
Like it just requires a little empathy and two seconds of creativity to come up with some other ways you could, depending on what they have, check that it’s their order — they could show their phone, any credit card with their name since they paid with an app, specific details about the order, approximately when they sent it in.
The restaurant could, or could not. It is certainly not "dystopian" though for a restauranteur to decide to save time and streamline by simply requiring verification that the person picking up the food is the person who paid for the food.
Like it just requires a little empathy and two seconds of creativity to come up with some other ways you could, depending on what they have, check that it’s their order — they could show their phone, any credit card with their name since they paid with an app, specific details about the order, approximately when they sent it in.