The website is very simple and straightforward. On the main page of the site, you only get to see the streaming tweets made by celebrities. There’s no way to filter celebrities. It won’t care whether you are a fan or not of a particular celebrity. CelebritiesThatTwitter will stream them anyway. As soon as the listed celebrity makes a tweet, the service will automatically display it. If you wish to go to the tweet page, simply click the name of the celebrity who made the Tweet. There’s also a Facebook and retweet button that you can use to share/retweet the messages.
This is one way of indirectly getting small info from celebrities themselves through Twitter. There’s no need for you to further saturate your Twitter account by following celebrities on Twitter. Instead of following them , you can simply view them at CelebritiesThatTwitter.