When you approve someone's Facebook friend request, you choose whether to allow them access to your full profile or your "limited" profile--a truncated version which presents only certain details to you. Other users make the same call when you initiate the request. If you're using Facebook chat and only want to chat with people whose full profiles you can see, customize your chat list to reflect this.
Log in to your Facebook account. Chat preferences are specific to user accounts, so you'll need to be signed in to modify them.
Maximize your Facebook chat list. Click the "Chat" button at the bottom-right corner of your screen, which causes a list of all your online friends to appear.
Hide limited profiles from your chat list. Click "Friend Lists," then click "Limited Profile" under "Display These Lists In Chat." Facebook will now hide all limited profiles from your chat list, unless you click the "Limited Profile" button again.