The only harm I see from participating in 0 ETH airdrops is no different than the rest of cryptospace. Meaning your investment may go to zero. (or stay at zero in this case)
It's unfortunate that there are many scammers dropping shitcoins in this way which gives this distribution method a bad rep, but it's essentially just a software (smart contract) controlled distribution. You could argue that it goes around many of the regulations and red tape other more legit coins need to deal with, but I don't think it makes it inherently less safe.
0 ETH airdrop is not worth to participate, just like you are sending zero ethereum transaction but you will get any shitcoin as a return for your transaction the fact that you will be lost on its transaction fees.
I remember my friend was paying around 0.000xxx ethereum to participate in the 0 ETH airdrop but that was getting some shitcoin that worth only not more than 0.0000xxx