I have been involved with a food bank for a long time. This is how we would approach this question (other food banks may vary etc):
Yes, food bank customers can express requests, eg halal, soft food (if toothless), no sugar (if diabetic), vegan, pet food etc.
If we happen to have a specialist item in stock, that someone has donated, then we will bend over backwards to match the item to the special request.
If someone is halal/vegetarian/kosher, which a lot of people are, we usually handle that by making up lots of generic vegetarian packages which would work for any of those customers - in other words the packages will exclude fish, meat and gelatin etc but probably won’t have specialist things like matzoh balls or tofu for example. They would be long on tinned chickpeas, fresh vegetables and tinned tomatoes, things like that.
It is highly unlikely that we would go out and buy special food for an individual requester, eg Oatly milk for a vegan. It is too time consuming and expensive. If we had the same request from a lot of people however, we might try to source a job lot via donation.
To give two examples:
During lockdown one shielding man asked for a Colin the Caterpillar cake for his birthday and it so happened that M&S had just donated a few Colin cakes that were about to go out of date. We matched the cake to the man and he was delighted, hooray.
In the run up to Eid we managed to source a large donation of dates from a local mosque, and these were distributed in packages for customers we knew to be Muslim.