How to disable json output from specific ansible commands?

Use no_log: true on those tasks where you want to suppress all further output.

- shell: whatever
  no_log: true

I believe the only mention of this feature is within the FAQ.

Example playbook:

- hosts:
  - localhost
  gather_facts: no
  vars:
    test_list:
      - a
      - b
      - c
    
  tasks:
    - name: Test with output
      shell: echo "{{ item }}"
      with_items: test_list
  
    - name: Test w/o output
      shell: echo "{{ item }}"
      no_log: true
      with_items: test_list

Example output:

TASK: [Test with output] ****************************************************** 
changed: [localhost] => (item=a)
changed: [localhost] => (item=b)
changed: [localhost] => (item=c)

TASK: [Test w/o output] ******************************************************* 
changed: [localhost]
changed: [localhost]
changed: [localhost]