It's not very very reasonable, because it can't be guaranteed. Even if you have shop bought cakes on the stand as well, they may have been prepared in a factory which also prepares nut products. If I make a cake, I may not include nuts but there are certainly nuts in my kitchen and we eat nuts a lot at home, which there is a small but possible potential to transfer into school.
I don't think it's reasonable to prevent nuts ever entering school property anyway, unless you also expect the same in every single public place you ever go (pub peanuts, cakes in shops, nut toffee, I can see what a nightmare it must be but is it realistic for these all to be banned?) I think it's reasonable for things to be labelled and for you to keep him away from the cake stall or provide nut-free cakes that you then eat yourself.
We were even asked to vet all the boxes used for making junk modelling, to see if they contained nuts. Obviously cereal boxes are the worst for this, I think the chance of a child making it through without encountering a nutty-traced cereal box is also quite low and it's best to prepare for it rather than assume everyone will be completely vigilant all the time as they may try but may also forget.
I think it's reasonable to have nut-free dinners and none in the lunch-boxes as you can't control that environment yourself, but you can control if your child eats off the cake-stand. My child couldn't have a cake off the cake-sale this week as they were going to after-school club and they are not allowed to all wander in. She had to lump it and I bought one later and gave it to her at home.
The concept of a nut-free school is quite problematic IMO, not because people aren't willing, but they don't see the myriad of hidden places you can have nuts. I think you are fighting a losing battle if you expect everyone to vet their cakes, bought or made, for nuts or nut oil. I would assume they do have nuts in and work from there.