Description of problem: MySQL-python project is dead, whereas mysqlclient is actively developed. mysqlclient is a fork of MySQL-python, so it should be the new upstream. You should simply replace mysql-python source code with mysqlclient source code, no need for a new package, use conflict things, etc.
MySQL-python-1.3.6-1.fc22 has been submitted as an update for Fedora 22. https://admin.fedoraproject.org/updates/MySQL-python-1.3.6-1.fc22
Package MySQL-python-1.3.6-1.fc22: * should fix your issue, * was pushed to the Fedora 22 testing repository, * should be available at your local mirror within two days. Update it with: # su -c 'yum update --enablerepo=updates-testing MySQL-python-1.3.6-1.fc22' as soon as you are able to. Please go to the following url: https://admin.fedoraproject.org/updates/FEDORA-2015-8790/MySQL-python-1.3.6-1.fc22 then log in and leave karma (feedback).
MySQL-python-1.3.6-1.fc22 has been pushed to the Fedora 22 stable repository. If problems still persist, please make note of it in this bug report.