This is not a hypothetical question. I particpated in two airdrops this year, Stellar and Byteball. I immediately sold the airdropped tokens and increased my bitcoin holdings by 3%. But I don't think Coinbase should be required to support Stellar or Byteball just because they did airdrops to Bitcoin holders.
Byteball in particular seems like just some guy's random project and only has value because of the current investment bubble in anything that looks like a cryptocurrency. I wouldn't trust it to be secure or work properly. What if Byteball is just a huge scam, and the creator can secretly mint tokens at will? Now Coinbase is participating in a scam!