Unable to add ICC color profile to ColorSync Profiles folder

An easy way to work around this is to simply create a ColorSync/Profiles path in your home folder. From the Finder, hold the Option key down while selecting the Go menu. This will show your Library. Choose Library from the Go menu and then release the Option key.

Once in your Library, create a new folder titled ColorSync. Open the ColorSync folder and create a folder titled Profiles. Move your Gracol profile into that folder.

Now, there is a limitation here. This will only be available to your user account. If the Mac in question has multiple users, you will need to do this in each user's home folder, as the preferences created within a home folder are only accessible to the user who owns the home folder.

Ok, if you need to add this to the main Library folder because this machine has multiple users, you will need to be an admin. I suspect your user account is a Standard account, thus the denial to write the file to this location. Contact your support team and ask that they add the file to the main library.

Hope this is helpful.

It has a circle with a line through it when I attempt to drop it into any of the color sync folders (including profiles).

A bit confusing in the wording there. The file you link to is:

GRACoL2006_Coated1v2.icc

Which is a profile. So I don't know what you mean by including profiles.

What am I missing or doing wrong?

My guess would be you're using your Mac from a guest account, or a standard account with intentionally limited access. You should be able to copy/move anything into or out of the main /Library/ColorSync/Profiles folder simply by supplying your admin password.