Note: On recent Fedora releases, this should no longer be needed
SELinux might become very unhappy if you try to run wine, but there's no reason to disable SELinux. You just need to tweak some SELinux booleans.
First, the one you most likely want is to set the wine_mmap_zero_ignore
sudo setsebool -P wine_mmap_zero_ignore 1
See man wine_selinux for more information about wine_mmap_zero_ignore.
Second another one you may encounter, which is more invasive is mmap_low_allowed,
see this bugreport on the Fedora bugzilla
for a discussion on the issue, and this wiki article on winehq
for information about it from wine's perspective. To enable it, run:
sudo setsebool -P mmap_low_allowed 1