Modify a symlinked INI file avoiding the Ansible's bug replacing the symlink with a copy of the target file

change_ini_file_preserving_symlinks.yml

- stat:
    path: /etc/example.ini
  register: example_ini_stats


# Defining the variable "actual_example_ini" containing the actual target file to be processed by ini_file
- set_fact:
    actual_example_ini: "{{ example_ini_stats.stat.lnk_target }}"
  when: example_ini_stats.stat.islnk is defined and example_ini_stats.stat.islnk
- set_fact:
    actual_example_ini: "{{ example_ini_stats.stat.path }}"
  when: example_ini_stats.stat.islnk is defined and example_ini_stats.stat.islnk == false
  
  
- name: "Trying to modify 'change_me' value in /opt/package/conf/example.ini"
  ini_file:
    path: "{{ actual_example_ini }}"
    section: "section"
    option: "change_me"
    value: "new value!"

Your tasks won't work when the file doesn't exist, and are quite lengthy.

- vars:
      example_ini: /etc/example.ini
  block:
    - stat:
        path: "{{ example_ini }}"
      register: result
  
    - name: Modify 'change_me' value in {{ example_ini }} or its target
      ini_file:
        path: "{{ result.stat.lnk_target | default(example_ini) }}"
        section: section
        option: change_me
        value: new value!

Amazing!

Thank you @flowerysong, much appreciated.