The GHSA has had some questions regarding the legality of a brand of non-traditional foot wear for cross country. Based on an NFHS ruling, a legal shoe "must be designed so that it can be fastened securely to the foot."
For more information, you can view shoes in question at www.vibramfivefingers.com.
The shoe (black) shown with the strap across the arch will be a legal shoe. The other example will not be a legal shoe for cross country.