@continuallychargingmyphone
The charity just hand out details to anybody of vulnerable families along with their contact details? 
Good point. It's bad. But also as bad, is allowing the families who are financially poor, to have the direct contact details of other families who have more money than them, and maybe more access to credit and so on.....
Both sides are put in a vulnerable position. Not just the 'poor' family. The financially better off family is at risk of being scammed or fleeced, or taken advantage of..... As appears to be happening to the OP! As has been said, it should definitely be anonymous.
I am not saying all 'poor' families will try and fleece more well off families, but it certainly could happen. As I said, it appears to be happening with the OP, with the family she has been linked up with, asking for 'special foods.
When it is getting to the point - as the OP has said - that you are being expected to support another family on top of your own, and continue it AFTER Christmas too then that's nothing but a piss-take.
Donating to a food bank should be little more than donating a few tins of soup, some washing powder, and some noodles, and maybe bathroom items like shampoo and shower gel etc... Them expecting you to support another family (and and adhere to their dietary requirements,) is very odd, and well out of order.
The OP needs to withdraw from it.