Can my kid's school ask for a copy of my divorce decree as proof of guardianship?

I'm in NY and, yes, the school can. It also protects you in the event the other parent attempts to pick the child up from school.

If you don't want to provide the entire decree, show the school the appropriate page.

I don't waive my decree around but I was recently asked to show it as proof of my last name - I showed the last page only.

The reason they are asking is to make sure you're the custodial parent. If you weren't then they may not be able to enroll your child without the other parents permission.

They can ask for proof that you are the custodial parent, so what they want is the child custody agreement, to show you have custody to enroll child in school

In my State - NY - the child custody agreement is included in the divorce decree. Often there is no separate custody agreement.