I don't think you'll find a different solution. Core Joomla will always be in favor of using user profile fields. Profile fields can be used for all sorts of information, therefore they are caught by the blanket ban in the Admin Tools feature. They will tell you -- very correctly in my opinion -- that you should not use the third party software's feature or talk to its developer, which you already did. Some may tell you it's a bug in Admin Tools, which is not, it's a preference. It's about noting what is your preferred approach: consistently preventing modifications of privileged users from the front-end or let them manage some / all of their profile preferences through the frontend? These are two opposing views. Only one can be applied to your site at one time.
I'd also like to point out that it's not just com_privacy triggering the Admin Tools protection. If you have, for example, Akeeba Subscriptions with its optional user profile integration you run into the same issue when a privileged user buys a subscription. The need to keep consistency of the user profile of privileged users overrides other needs of the site.
Hence my recommendation to have your backend user go through the backend first to accept the privacy policy. This is the correct way to deal with it. If you want to be consistent in enforcing a policy of non-modification of privileged users through the front-end of the site you need to cooperate with the privileged users of your site.
Nicholas K. Dionysopoulos
Lead Developer and Director
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