Generally when I do this on multisite I have one master site where I edit all field groups. I make sure that I have downloaded all of the field groups after any changes.
Usually, I just activate the theme on new sites, the existence of the json files means that the field groups will be active on the new site without importing them.
In some cases I create new sites by duplicating an existing site. In this case I go into the admin of the new site and delete all of the field groups from ACF. This has an unintended site effect of deleting the json files. But then I just upload them to the theme. If I do this I generally do it when I’m sure no one will be active.
Another option is to disable the ACF admin on all but the master site where I make any changes. https://www.advancedcustomfields.com/resources/how-to-hide-acf-menu-from-clients/
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