Oh well, it was a first guess because Registry Cleaner will clear font references.
Just to be sure here, you are certain that it is CCleaner that is removing them?
From my reading it seems that the favourite fonts not working as it should and losing it's 'stars' is not an uncommon problem in photoshop.
Assuming that it is CCleaner removing them:
I take it that the fonts themselves are not being removed and having to be reinstalled, just the favourite links to them are going missing?
In which case it's a matter of finding out where photoshop is saving those links and then making them (or the folder) an exclude in CCleaner.
From a quick online search I believe that it's in the folder- <em>C:\Users\[user name]\AppData\Roaming\Adobe\Adobe Photoshop <version>\CT Font Cache\</em>
See: <a href="https://helpx.adobe.com/uk/photoshop/kb/troubleshoot-fonts-photoshop.html" rel="external nofollow">https://helpx.adobe.com/uk/photoshop/kb/troubleshoot-fonts-photoshop.html</a>
(You will have to turn on 'hidden items' in File Explorers View menu to see the 'AppData' folder and below in File Explorer).
So make that folder an Exclude in Custom Clean: https://www.ccleaner.com/docs/ccleaner/using-ccleaner/excluding-files-folders-and-registry-entries
Note that Excludes, and Includes, only work in Custom Clean, Health Check ignores them.
Alternatively, (or if Excluding that folder doesn't work):
In CCleaner set Options>Advanced to show the File List rather than the Advanced Report
In Custom Clean right click each of the entries that you currently have ticked and 'Analyze' from the popup menu.
Then look at the files found for anything obviously photoshop related.
When you see a file that is obviously photoshop related right click on it and 'Add to Exclude list'.
Go through them all (except the browsers?) because there may be photoshop stuff in more than one category.