Nothing, there is nothing that anyone should worry about. If anything, you might have a day of confusion if the fork went really off the chain, lol. There is nothing that is going to hurt your wallets, although a trusted online wallet is the easiest place to ride a fork out as that leaves the site to deal with any issues and not you. But, make sure that you really trust a site, because potential scammers love to use excuses like this is bail with their clients wallets.
Forks have happened before and he is right that there is nothing to worry. The best thing that we could do is to hold our coins because after the fork, the price of bitcoin will eventually rise and that will give us profit. Bitcoin will be agfected but I am sure that after a few days or weeks, the price will be back to normal or might even get higher.