Basically, you've discovered 2 triggers (Photos/iCloud synching etc. plus running an external monitor) for this issue. It's possible that both activate the same gremlin that messes up (technical term) the video hardware in a way that gets manifested as blurred/ghosted fonts on the local screen. I'm not sure why only the local screen would be affected, other than the fact that it has it's own physical (non-DVI?) connection and the video hardware probably sees them as physically separate video outputs.
While I do have an embedded system background, I can only take a guess at what is happening, which is that each trigger results in an incorrect setting being written to the configuration register for the local display. Basically, a bug which causes the video controller to mess up (technical term) the alignment of the pallettes or something. Perhaps the developer was unaware that the configuration registers aren't identical, and wrote the same value to both registers, causing unexpected behaviour on the local display, somewhere on the 2 identified paths.
Not much you can do about the bug, other than try to avoid triggering it. Turning off Photos/iCloud synching avoids the 1st trigger. Not sure how you can avoid the other one.
Two options: put up with it and hope that Apple provides a fix, or roll back to El Capitain - which might cause problems with your Photos and iTunes libraries. I think I would cross my fingers and hope there is a fix available soon.