I'm not. Maybe I should be, but I don't think so. A hard fork means there are two sets of people who have different rules for what makes a block acceptable. Each set will view all the coins in any private key as available to whoever holds the private key. If you don't hold the private key, then remember that a third party is a huge security hole, and concern is more appropriately for that hole than for the hard fork.
When you spend coins, I suspect that most of the time, both sets of people will accept the transaction into their blockchain, but one of them might not. In that way, whoever is supposed to be getting your btc will only get them in the view of one set of people. You can then do research to see how to get the other group of people to accept your payment, which shouldn't be too hard. They will be providing software in which you still hold the btc, and you can use that software to send the same payment to the same address.
There is another way to satisfy the person to whom you send the bitcoins if they only received them on one fork. This is to convince them that the coins on the other fork are not very important and they can be ignored. This actually happens every time a block is "orphaned" which means that two miners solved a block so closely in time to each other that we got two valid blocks at the same block height. Each miner in the mining community chooses which block to use as the "head" and builds on it. Any transaction that was in only one of the two valid blocks is (generally) automatically rebroadcast to the network so that it can get into the next block. In a hard fork situation, it will not be automatic.
If you do convince the other person that it isn't important, you then have the opportunity to be a stand-up person and do the work to get your transaction into the other blockchain. Even if you send them to someone who has chosen to accept coins on the other blockchain, you can still be a stand-up person by ensuring that the receiver agrees to accept the bitcoins only on the one blockchain and has no expectation of getting them on the other one.
One of the reasons I love cryptocurrencies so much is that they provide us with myriad opportunities to demonstrate that we are good honest people. Yes, I have been scammed many times, by a few people, but I understand the availability heuristic, so I know that the picture of humanity that scammers paint is wrong. They are the rare (but, in bitcoin, highly active) vermin among us, fooling our as-yet-unsophisticated brains into mis-perceiving their depravity as a common among humans, instead of common among parasitic humans.
I think school does the same thing to us by presenting a world mostly of people who are quite immature, and we end up thinking such immaturity is a common human trait. School actually creates that result, as far as I can tell.
My comments here are intended to be helpful advice regarding all hard forks in all cryptocurrencies. You can examine the history of ETH and BTC to see hard forks in the past and check to see if my claims are true. You may already see flaws in what I have presented here, and if so, please mention them in a comment so I have a chance to address them.
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Thanks to Rules for Rebels for this video that explains hard forks.
I'm not worried either. Each coin will have their market and value. It's only people who use bitcoin daily who will worry in the short term on the technical aspects of dealing with a fork. Those who can wait can wait for the community to solve and educate on any technical problems, in most cases I see people getting two different coins and eventually more value. Could cause many bitcoin investors to own alt-coins for the first time in their lives!