how to make a case-insensitive graphql query?

Names in GraphQL are case-sensitive, as per the spec. Names include field names, type names, variable names etc.

So, in short it is not possible to do it.

Using the _ilike operator makes the query case-insensitive.

query MyQuery {
  heroes(where: {name: {_ilike: "%baTmaN%"}}) {name, movie }
}

Source & documentation: https://github.com/hasura/graphql-engine/issues/1516