This problem has been isolated to a combination of how Samba interacts with Windows and how the new library component used in 8.1i interprets the security setting. In effect, World permissions from the UNIX drive are being passed on to every group for the mapped drive on the Windows machine.
This issue has been fixed in ISE 8.2i.
In the meantime, there are two possible ways to work around this issue:
1. Map the Linux or Solaris drive through a Windows server - NAC mount.
2. Give write permission to World for the network drive directory being mapped. In this case, creating a new project will still produce a warning stating that the directory is Read-Only. However, the project will be successfully created.
NOTE: If this error is issued while creating a project on a drive that is not mounted through Samba, check the directory security settings on the Windows machine. If Deny is selected for any of the user's groups in the security options for the folder in question, this error will be correctly issued.
See also (Xilinx Answer 23341)