Some people are getting their cards laminated. I opted not to do that because of the likelihood we'll need a 3rd or booster shot and I want access to the card to add that next shot. So I got clear vaccine card holders, you slip the card in and there's a closure, but you can still pull it out later on if you need to.
If you go this route, just be aware that CDC cards come in at least two sizes. The petite size will fit into any of the advertised 4x3 holders you can find (Etsy and Amazon have loads of them), but the bigger size, it's a much tighter fit. You might be able to fit it with a little maneuvering (basically slightly bending the top to slip it in, it fits cleanly, but it's a seriously tight fit that way). The only other option I've found thus far s 2 inches larger, so unnecessarily bigger for carrying around all the time, and that is a clear passport holder (go with 4x6).
I didn't touch my vaccine card for the month in between appointments, just stayed in my wallet the entire time. And it definitely was looking less than pristine come the second vaccine appointment. You definitely need something to keep it safe.