To remove record type in Chatter Free and Chatter Moderate User, it’s not that straight forward because there is no Object Settings in Profile Overview. You need to hack URL.
Use this format to generate a URL to access Object Settings in a profile:
https://[your org].salesforce.com/setup/ui/profilerecordtypeedit.jsp?id=[Profile ID]&tid=[Object TID]&pn=[Profile name and use "+" to replace blank]
Get Profile ID
When you click on a profile, Profile ID can be found on URL.
For example, when click on Chatter Moderator User profile, the URL is:
The Profile ID for Chatter Moderator User is 00e90000000pbIg
Get Object TID
When you click on a Custom Objects, Object TID can be found on URL.
For example, when click on Incident custom object, the URL is:
The Object TID for Incident is 01I90000001hppQ
For standard objects, use the name of the object instead e.g. Account.
To access Chatter Moderator User‘s Incident object setting, use:
Replace Chatter+Moderator+User with Chatter+Free+User if the profile is Chatter Free User.