Is there a script, or some other solution, that will auto-Allow Access in a spreadsheet?
The only solution is that the owner or any editor do the mandatory authorization for each of the external spreadsheets.
Google Apps Script doesn't include any class or method for Google Sheets built-in functions, so the authorization should be done on the Google Sheets UI by the owner or an editor of the spreadsheet.
The good news is that the access authorization is required only one time by external spreadsheet, so you could add a sheet having something like
=IMPORTRANGE(url,"A1") for each spreadsheet, authorize the access to each one, and after that delete that sheet.
Note: The user who granted the permission should not be removed from the sharing settings.