When does “Initialize Git repository” start checked?

The checkbox is context-sensitive. For a new folder in an ordinary directory it starts on, because a new gem usually wants its own repository, and that is also what makes isolated shards possible. When the new folder would sit inside an existing repository, it starts off, so crystl does not nest Git history into a monorepo or a folder that already has version control. Either way the choice is yours before the gem is created.