Will a SHAKE128 stream cipher be vulnerable to related key attacks? Suppose that SHAKE is seeded with key concatenated to an IV, will the 'key' stream produced by SHAKE128 vulnerable to related key attacks like RC4 is? 

My guess is no because seed is already "absorbed" before the key stream is "squeezed" out.
There is no way to know for sure, but it seems unlikely to me.

SHAKE128 is an extendable output function, basically a hash function with variable output. It must be secure with completely attacker controlled input. If you use it to build a stream cipher (perhaps using KMAC (draft pdf), which is supposed to be PRF), it seems unlikely that related keys would be a concern without the hash function use case also being broken.

However, the security goals of hash functions and stream ciphers are different and SHA-3 itself could be broken, so only time will tell.


  My guess is no because seed is already "absorbed" before the key stream is "squeezed" out.


This particular argument does not really make sense, since RC4 also absorbs the key first and only then produces output. Yet it is vulnerable to related key attacks.