So, before answering the question, let's review what a browser cache is. You know about the StackExchange logo that appears at the top left of the webpage? It would seem silly to retrieve the information for this logo image from the server every single time you access a Super User webpage. The browser cache is simply space in your hard drive to store such data so that it the webpage with redundant data loads faster.
Alas, as of right now there is no way to make internet speed faster than hard drive speed. Therefore, the browser cache exists.
When you clear your browser cache, you clear up a considerable amount of space on your hard drive. Again, as you have mentioned, this signs you out of most sites. However, there is a specific piece of data that you may have failed to delete: cookies.
Cookies are little bits of metadata about a webpage, and are not included by default in the data that CCleaner deletes. So when you delete your cache, alas, you do not delete a few of the cookies. The solution to this is to manually clear out your cookies from your hard drive with Windows Explorer (I'll assume you use Windows).
The location for such cookies depends from browser to browser. The cookie location for Chrome is here:
C:\Users\<your_username>\AppData\Local\Google\Chrome\User Data\Default\
This is described more in data in the answer to this specific question about Chrome cookies.
To delete, close the Chrome browser and delete all processes associated with Chrome. If you don't then Windows will lock the files because they are still in use by those processes. Then, go to the location mentioned above and delete the cookies manually. This should sign you out of Facebook and all other sites that you mentioned.
1Have you deleted your cache and cookies using Chrome settings? I imagine it must be that CCleaner is not working right or has an option to not clear cookies for certain sites. – Appleoddity – 2018-12-10T04:45:05.800