After the fork, there are two separate coins.  You can deposit either Bitcoin from a Bitcoin wallet, Bitcoin Cash from a Bitcoin Cash wallet, or you can separately deposit both...no different from depositing Bitcoin and Ethereum.  You only get "free" Bitcoin Cash if you own Bitcoin before the fork and you have the private keys or the 3rd party (e.g. Kraken) that has your keys provides you a way to get access to your Bitcoin Cash.  If your 3rd party is something like Coinbase/GDAX, then they are saying that you won't get your Bitcoin Cash.  Even 3rd parties that announce that you will get access to your Bitcoin Cash could potentially mess up if they haven't thoroughly vetted and tested all processes, so there's risk there.  If you have your private keys, then you control all the risk and you only have to deal with your own mistakes (i.e. not properly securing your keys, etc.) and won't be victim to someone else's.  The sage advice people are giving to make sure you control your private keys assumes that you are capable of properly securing them.  If that's not the case, storing them with a 3rd party wallet or exchange could potentially be safer.