From the Salsa20 security document, DJB states that he doesn't care about related key attacks:
The standard solutions to all the standard cryptographic problems—encryption, authentication, etc.—are protocols that do not allow related-key attacks on the underlying primitives. I see no evidence that we can save time by violating this condition. The reader might guess that Salsa20 is highly resistant to related-key attacks; but I simply don't care.
Emphasis mine. The only related-key attack I know of is against Salsa20/7 and requires 2217 operations using 224 pairs of keystream blocks from two sets of keystream. I can't find any attacks on ChaCha. The linked paper cites a discussion from the eSTREAM forums which argues the attacks are irrelevant.
What is the state of Salsa20 and ChaCha security against related key attacks? What can be said about their design that would make them resistant to such attacks? How does ChaCha compare to Salsa20?