Taxonomy is a good feature on SharePoint 2010. It is normal, so, you want interact with this kind of fields programmatically. What you should know is that if you are working on a publishing web site and you have a full anonymous web site some configuration is required.
By default only [AUTHENTICATED USERS] have access to the hidden list /Lists/TaxonomyHiddenList/ Sharepoint uses to store the values and make the queries.
To allow Anoymous user to access on it follow the steps below:
1) Browse the Public web site (normally a SharePoint extension)
2) Try to access to the list Lists/TaxonomyHiddenList/AllItems.aspx. The system will ask you to authenticate.
3) Click on List Permission on the tab List.
4) You will be redirected to a page where you have the icon Anonymous Access (image below). Be careful, if you try to access to the “authenticated web site” you will not have this button. You are now able to set the Anonymous permission.
Your web site will be work fine even using Taxonomy