In the old Azure portal, you could simply stop a "Classic" Linux VM without doing waagent -deprovision+user, and then create a snapshot from it.
That snapshot could then be succesfully used to create new VM instances. But, as I found out the hard way, this does not work with Azure Linux VMs through the new portal / new style VMs.

So I ended up with a VM image that can only created un-bootable VMs, AND the template VM itself could not be started anymore because it was generalized. The well-known error "Failed to start virtual machine 'templateVM1'. Error: Operation 'start' is not allowed on VM 'templateVM1' since the VM is generalized." occurs when I try to start the VM.

Luckily, I found a simple way to bypass the "since the VM is generalized"  message.

1) go to the "Disks" page in the Azure Portal: