This error message is because the ‘Show in expense claims’ box for the category has not been ticked in your Chart of Accounts in Xero.
To resolve, please go into your Xero account. Go to Accounting > Advanced > Chart of accounts. Here you can click on the relevant Category and, once open, tick the Show in expense claims box.
After doing this, don’t forget to reload your categories list and try to republish the affected items (even though the error message may still appear).