This kind of trigger AJAX functionality does not yet exist for the ACF plugin.
You can however, use the relationship field to filter the posts by a taxonomy.
However, you will not be able to save the taxonomy as a sub field value.
This said, it would be possible to write some custom jQuery which triggered a custom AJAX call on change of the taxonomy select field. Your AJAX call could then query and return post data which you would then update the post_object field with.
Hope that helps.
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