To use the meal analogy, the Dungeon Master is tasked with creating a menu with several choices from which to select, but it is not reasonable to expect the Dungeon Master to create a menu with infinite choices. For the sake of example, let us assume the DM prepares an "Italian" menu offering both marinara and alfredo-based sauces, several types of pasta, several types of protein (chicken, beef, pork, etc.), salads, and pizzas. That is a reasonably diverse menu to provide, no?
Once the Dungeon Master has presented the menu to the players, it is reasonable to expect them to select something from the menu provided. It is also reasonable to expect them to choose to "dine" elsewhere if the menu is not to their taste. (For example, it is not reasonable for me to demand a burrito at an Italian restaurant; if I want a burrito, I should look for a restaurant offering a "Mexican" menu).
It is also reasonable for a player to explore the possibility of ordering a custom item, up to and including ordering off-menu. However, if the player elects to explore the possibility of ordering completely off-menu, it is ALSO reasonable to expect the DM to decline to prepare something off-menu (i.e., I can ASK for a Burrito, and maybe the chef of the night happens to have tortillas and beans on hand and is willing to cook one for me; however, I should not be offended if I ask for a Burrito and am informed me that order cannot be filled as this is an Italian restaurant and no tortillas or beans are on-hand). At this point, my choices return to ordering on-menu or leaving with no ill will.
There may be some requests for ingredient changes that I can easily handle (e.g., "I am vegetarian; please forgo the protein and serve me pasta with sauce only") or requests for items that are not off-menu but could be reasonably accommodated (e.g., I know your menu doesn't have Calzones, but that uses all the same ingredients as a pizza; can you just change the shape of the pizza please?")
Neither the ask nor the response is necessarily indicative of bad faith (some asks are made in bad faith of course, but not all are); however, a refusal to allow someone to go off-menu should not be taken as unreasonable as it is impossible for a chef (or a DM) to have foreknowledge of the tastes of all customers (players) beforehand and often even less possible to prepare something for all of those tastes. There is a certain limited band of tastes for which you can prepare. Similarly, players should know that even requests they find reasonable may not be possible for reasons beyond their control ("I'm sorry, sir, we serve thin-crust pizza and the oven aperture is flat and thin; folding the dough into a Calzone is possible, but fitting the folded Calzone through the aperture is not, so we cannot accommodate your request"). The question of how reasonable it is to go "off menu" cannot rest with the players as they are not familiar with the framework for serving, it must rest with the DM since the DM has created the framework. The DM should make a good-faith effort to fulfill reasonable requests, but it is for the DM to determine what is "reasonable." Similarly, it is for the players to determine if a DM is "unreasonable" and if they find the DM unreasonable, it is their opportunity to leave and find a new DM to work with that is more to their liking. There ought to be give and take both ways here, but ultimately, the DM's number one job is "judge" and so the DM is given the role of "final arbiter" of what is reasonable in this negotation.
For example, I would have a hard time dropping a Rifts Glitter Boy in the middle of my D&D campaign. I would suggest instead that the player that wants that should be in a Rifts campaign instead. This is of course an extreme example versus, say, allowing Aarakocras or Tortles as PCs, but there is a limit to the amount of prep I can do as a DM, and if I have been asked to create a setting/campaign in which to play, it is expected that I will have thought of history, politics, races, etc. so it is not unreasonable to ask the players who will be playing with me to limit their choices to things I have contemplated for the setting. They may of course ask to go off-menu and I may be willing to work with their off-menu request, but the bulk of the work of preparation almost always falls on the DM rather than the players, and as a player I ought to be respectful of the additional work my request to go off-menu causes and recognize that such a request may be reasonably denied.