How can I use a regex on a mysql response to filter values using ansible?

If you want to extract the value of Slave_IO_Running, you can do something like this:

    - set_fact:
        slave_io_running: >-
          {{ (yum_sec_upd.stdout_lines | select("search", "Slave_IO_Running:") | first).split(": ")[1] }}

This will set the variable slave_io_running to the extracted value. Here's a complete test showing this in action:

- hosts: localhost
  gather_facts: false
  vars:
    yum_sec_upd:
      stdout_lines:
        - '            Slave_IO_Running: Yes'
        - '            Slave_SQL_Running: No'
        - '              Replicate_Do_DB: '
        - '          Replicate_Ignore_DB: '
        - '           Replicate_Do_Table: '
        - '       Replicate_Ignore_Table: '
        - '      Replicate_Wild_Do_Table: '
        - '  Replicate_Wild_Ignore_Table: '
        - '                   Last_Errno: 0'
        - '                   Last_Error: '
        - '                 Skip_Counter: 0'
        - '          Exec_Master_Log_Pos: 2595'
        - '              Relay_Log_Space: 1306'
        - '              Until_Condition: None'

  tasks:
    - set_fact:
        slave_io_running: >-
          {{ (yum_sec_upd.stdout_lines | select("search", "Slave_IO_Running:") | first).split(": ")[1] }}

    - debug:
        msg: "running"
      when: slave_io_running

    - debug:
        msg: "not running"
      when: not slave_io_running

(Tested with ansible ansible 2.12.1)

Create a dictionary

stats: "{{ yum_sec_upd.stdout_lines|map('from_yaml')|combine }}"

gives

  stats:
    Exec_Master_Log_Pos: 2595
    Last_Errno: 0
    Last_Error: null
    Relay_Log_Space: 1306
    Replicate_Do_DB: null
    Replicate_Do_Table: null
    Replicate_Ignore_DB: null
    Replicate_Ignore_Table: null
    Replicate_Wild_Do_Table: null
    Replicate_Wild_Ignore_Table: null
    Skip_Counter: 0
    Slave_IO_Running: true
    Slave_SQL_Running: false
    Until_Condition: None

The condition is trivial then

    - debug:
        msg: Slave IO is running
      when: stats.Slave_IO_Running