Hello, is there a way to keep a group of Accounts or Contacts private to a Profile or Role regardless of sharing settings that may open up Accounts/Contacts to other profiles and roles?

Depending on your sharing rules - there are a few options.   You can create a checkbox, picklist, record type, whatever is suitable for you, and once a particular value is selected, you can exclude that from sharing rules.   If role hierarchy is turned on, sharing will still happen. Options to stop that - turn off role hierarchy or exclude the roles you don`t want to share from the hierarchy but that`s not recommended solution.   You can set automation to select your value if you have specific criteria.