Adding the computed_fields field in the manifest resource and appending the stringData solved the issue. The resulting kubernetes_manifest is

resource "kubernetes_manifest" "default_user_config" {
  computed_fields = ["stringData"]
  manifest = yamldecode(<<EOF
apiVersion: v1
kind: Secret
metadata:
  name: "default-user-config"
  namespace: ${var.namespace}
type: Opaque
stringData:
  default_user.conf: |
    default_user = user
    default_pass = password
  # host: dmF1bHQtZGVmYXVsdC11c2VyLmRlZmF1bHQuc3Zj
  # username: my-admin
  # password: super-secure-password
  # port: "5672"
  # provider: rabbitmq
  # type: rabbitmq
EOF
  )
}