I had the exact same problem.
I used the Terminal.app to change my folder rights as explained by @Ravi Kiran. Problem, at the step 2 (sudo chmod -R 777 /Users/myUserName/Library/Caches/Adobe\ InDesign) I got this message :

/Users/myUserName/Library/Caches/Adobe InDesign: No such file or directory

I don't know why, but the folder Adobe InDesign was missing in my Caches folder of my Library. Luckily for me, I ask a friend (who has the Creative CC too) to send me his own Adobe InDesign folder (/Users/myFriendUserName/Library/Caches/Adobe InDesign). I copy his folder on my computer at the right place (/Users/myUserName/Library/Caches/) and InDesign CC 2018 worked again!

Voilà!

I had the same issue for a few days (24th May, 2018). In that time I tried uninstalling and reinstalling older versions.

In the end, what got it working was changing the permissions in
~/Library/Preferences
~/Library/Application Support
and ~/Library/Caches

I ran into this today (5/2/2018). First of–screw Gatekeeper and High Sierra permissions. I get the theory behind, but don't roll it out until its actually ready.

Secondly—go into terminal and run:
cd ~/Library
then:
chmod 777 Caches
chmod 777 Preferences

Restart your computer and open inDesign.

NOTE: This process has also worked for me with numerous other programs that don't get along with High Sierra in case you run into others. Always set 777 on Cache (not sure why it gets reset to not 777) and then whatever folder you get the error on.

I'm having the same issue. Have tried deleting preference folders in ~/Library/Preferences and ~/Library/Application Support. No difference.
Doesn't work. Now what?

Fix please Adobe.

Same problem. I went to ~/Library/Preferences at cleared those preferences and I don't see anything for Adobe Indesign in ~/Library/Application Support or Caches either (but that's probably because I run CleanMyMac3).

Been unable to use Indesign for two weeks now, which is unacceptable as a professional designer. Please help me resolve this.

You need to set permissions for the ~/Library/Caches folder as well. This solved it for me.

I have a similar if not the same issue. I get the following prompts when i try to open my file.

This file is already open by another user or another application. This file may be stored on a network server and cannot be open until the other user closes it.

Same for me! Fix please

Had this problem for a couple of my users today (I work in IT).. Going into ~/Library/preferences and ~/Library/Application Support and manually deleting the preference folders for each of the adobe ones. It asked for admin permissions to delete (which it shouldn't in user directory libraries) but when the app re-opened it worked fine.

This clears your preference setups though.

I'm having the same issue. Any fix yet?

Same

have the same problem over here ; Kan Adobe InDesign niet starten omdat u niet genoeg rechten hebt voor toegang tot de mappen met voorkeuren. Controleer of u de juiste rechten hebt en start Adobe InDesign opnieuw. iMac (27-inch, Late 2013) mac OS high Sierra

I'm having the same issue! I've tried everything my IT staff has suggested, to no avail. They are just as stumped as I am.

Same here!!! Modifying folder permissions does not help.

This started happening to me this morning. Any update?

Any solution?

It just started happening to me today, any solution yet?