How do I set register a variable to persist between plays in ansible?

The problem you’re running into is that you’re trying to reference facts/variables of one host from those of another host. You need to keep in mind that in Ansible, the variable app_git_sha1 assigned to the host localhost is distinct from the variable app_git_sha1 assigned to the host main or any other host. If you want to access one hosts facts/variables from another host then you need to explicitly reference it via the hostvars variable. There’s a bit more of a discussion on this in this question.

Suppose you have a playbook like this:

- hosts: localhost
  tasks:   
    - command: /bin/echo "this is a test"
      register: foo


- hosts: localhost
  tasks:
    - debug: var=foo

This will work because you’re referencing the host localhost and localhosts‘s instance of the variable foo in both plays. The output of this playbook is something like this:

PLAY [localhost] **************************************************************

GATHERING FACTS ***************************************************************
ok: [localhost]

TASK: [command /bin/echo "this is a test"] ************************************
changed: [localhost]

PLAY [localhost] **************************************************************

GATHERING FACTS ***************************************************************
ok: [localhost]

TASK: [debug var=foo] *********************************************************
ok: [localhost] => {
    "var": {
        "foo": {
            "changed": true,
            "cmd": [
                "/bin/echo",
                "this is a test"
            ],
            "delta": "0:00:00.004585",
            "end": "2015-11-24 20:49:27.462609",
            "invocation": {
                "module_args": "/bin/echo \"this is a test\"",
                "module_complex_args": {},
                "module_name": "command"
            },
            "rc": 0,
            "start": "2015-11-24 20:49:27.458024",
            "stderr": "",
            "stdout": "this is a test",
            "stdout_lines": [
                "this is a test"
            ],
            "warnings": []
        }
    }
}

If you modify this playbook slightly to run the first play on one host and the second play on a different host, you’ll get the error that you encountered. The solution is to use Ansible’s built-in hostvars variable to have the second host explicitly reference the first hosts variable. So modify the first example like this:

- hosts: localhost
  tasks:

    - command: /bin/echo "this is a test"
      register: foo


- hosts: anotherhost
  tasks:
    - debug: var=foo
      when: foo is defined

    - debug: var=hostvars['localhost']['foo']
      when: hostvars['localhost']['foo'] is defined

The output of this playbook shows that the first task is skipped because foo is not defined by the host anotherhost. But the second task succeeds because it’s explicitly referencing localhosts‘s instance of the variable foo:

TASK: [debug var=foo] *********************************************************
skipping: [anotherhost]

TASK: [debug var=hostvars['localhost']['foo']] **************************
ok: ['anotherhost'] => {
    "var": {
        "hostvars['localhost']['foo']": {
            "changed": true,
            "cmd": [
                "/bin/echo",
                "this is a test"
            ],
            "delta": "0:00:00.005950",
            "end": "2015-11-24 20:54:04.319147",
            "invocation": {
                "module_args": "/bin/echo \"this is a test\"",
                "module_complex_args": {},
                "module_name": "command"
            },
            "rc": 0,
            "start": "2015-11-24 20:54:04.313197",
            "stderr": "",
            "stdout": "this is a test",
            "stdout_lines": [
                "this is a test"
            ],
            "warnings": []
        }
    }
}

So, in a nutshell, you want to modify the variable references in your main playbook to reference the localhost variables in this manner:

{{ hostvars['localhost']['app_git_sha1'] }}