Why does cloning (via ssh) my own repository from github require my passphrase?
So as a consequence: Would it be a huge safety-issue if I generate some ssh keys without a passphrase (for working on small opensource projects)?
Because your SSH client cannot decrypt your key without knowing the passphrase, and without a decrypted key it cannot connect to the server and run
Not much, as long as you keep your computer secure (both physically and otherwise).
However, one key for all Github usage should be enough. Most SSH clients have an "agent" program that allows keys to be unlocked once and kept in memory: GNOME Keyring,