This isn't really a React-specific tip, as such anti-patterns often occur in code in general; in this case, React simply points them out more clearly.
Using props to generate state in getInitialState often leads to duplication of "source of truth", i.e. where the real data is. This is because getInitialState is only invoked when the component is first created.
Whenever possible, compute values on-the-fly to ensure that they don't get out of sync later on and cause maintenance trouble.
Bad ex