Duplicate allow_in_bindings Option in JSON When Modifying Field Groups in Child Theme

Description:

We are experiencing an issue when setting up a parent theme with customized ACF fields in the child theme. When a field group from the parent theme is modified in the child theme, it sometimes leads to the allow_in_bindings option appearing twice in the JSON file of the field groups.

Steps to reproduce:

1. Set up a parent theme with customized ACF fields.
2. Create a child theme and modify an existing field group from the parent theme.
3. In the JSON file for the field groups, the allow_in_bindings option appears twice.

Expected Behavior:

The allow_in_bindings option should only appear once in the JSON file, with the correct value based on the parent theme's field settings.

Actual Behavior:

If the parent theme has set allow_in_bindings to 0 (false) for a field in a field group, the child theme adds the allow_in_bindings option again with the value set to 1 (true), causing a conflict.

Additional Information:

• This issue occurs when modifying field groups inherited from the parent theme in the child theme.
• It seems that the child theme is not respecting the parent theme's settings for allow_in_bindings and overwrites the value.

Version Information:

• WordPress Version 6.7.2
• PHP Version 8.1.32
• ACF Version ACF PRO 6.3.12
• Browser Chrome Version 134.0.6998.166

Start by reproducing the parent-theme and child-theme field-group setup described in the issue using ACF PRO 6.3.12, then inspect where the field-group JSON is generated or merged. Done means the JSON contains one allow_in_bindings option and preserves the parent value of 0 when the child modifies the field group.