What will sometimes work is to ask for something else. The best thing is something which you know you can have, and which is quite certain to be available. The easiest thing is a glass of water. Or a cup of tea.
Thank you, but I really cannot eat that much right now. Could I just have a glass of water/cup of tea, please?
The reason why this can work is the symbolic part of hospitality being discussed here. Feeding a guest is a hospitality ritual, and refusing to participate in the ritual has social consequences. When you don't play your part, some hosts will assume the worst and feel insulted, but most will just prompt you again like a good suffleuse, giving you yet another opportunity to "get back on track" and fulfill the ritual.
By asking for something else, you are leading the ritual to a less traditional version, but you are not breaking it outright. The exchange of victuals still takes place, and there is less of a chance that the host will feel that there is something "wrong" with the visit.
This is not a surefire thing, it depends on how much the host is invested in, for lack of better word, the purity of the tradition. For some it will feel like they have fulfilled the script, for others there will still be the impulse to do it with food because the water is not "sufficient" to replace the ritual.
This is also what makes it rather difficult to decide what to ask for. On the one hand, if it is too "simple" like water, it may not be elaborate enough for the purpose (they will bring you the water and still insist that you eat). On the other hand, if you ask for something which is closer to what they imagine should be offered to a guest (maybe "do you have an apple, or some other raw fruit?") and they don't have it, they will feel guilty for not being able to fulfill your wish. You may have to try different approaches with different hosts and see which is better on average, and maybe learn which one works with whom.
As a long-term strategy, if you frequently visit the same hosts, you might find a way to tell them that you absolutely love X, where X is some kind of food that is safe for you (a brand of chocolates, or raw apples, or something else), and that you would love it if they could have some at your next visit. Unless you happen to choose something which they disapprove of in principle (like a luxury brand of chocolates when the host is a frugal person), this kind of demand is not impolite, but rather it makes them happy to know that they are not just feeding you, they are also feeding you a thing you love! Especially if those people are your elderly female relatives, it is probably the best way they know to express their affection for you.