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 'Settings' in Xero and then select 'Chart of Accounts'. Here you can click into each category and then tick '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).