Bloom, I'm a kinder teacher and that amount of restrictions annoys me too!
Yes, it's realistic to request no nuts of a child has anaphylaxis but its ridiculous if any of the foods you've listed are just allergies.
If they are just allergies then the centre should be putting in place risk minimization plans. Eg the child with allergies has a tray they use at the table to eat their food, everyone is educated in not sharing food etc.

There are some great resources on the allergy facts website as well as the ascia website. If you'd like further clarification on what is ok for the centre to implement you could call the Department of Education and Early Childhood Development.

For childcare:

http://www.education.vic.gov.au/chil.../concerns.aspx

For kindergarten:

http://www.education.vic.gov.au/chil.../concerns.aspx

Eta- I've just seen you're in Queensland so will try to find a number for you.

Eta 2- http://deta.qld.gov.au/earlychildhood/