Depends on the site security. Password protection for the campground's wifi affords zero protection for your data. All it does is keep unauthorized users off the network, your computer sends data unencrypted, so anybody with a radio nearby can catch it all, they just can't log into the network.
On the other hand, banks and similar sites are supposed to be secure.
If you want to be certain of your security, you need to use a VPN (virtual private network). This requires a little software on your end plus a subscription to a VPN server. This will establish a fully encrypted connection between you and the VPN server, which then connects via the internet to wherever you are going. But all data to/from your computer will be encrypted.
How much security you need is a matter of opinion.