The issue isn’t as big of a problem as some of the media made it sound (I think initially there was some confusion about exactly what was happening) and the issue is not that the watch will connect to random WiFi networks either. The watch will only connect to known WiFi networks that you have connected to with your phone.
The problem happens when there is a known WiFi network that has an interstitial login (where you get redirected to a webpage where you need to enter information or agree to terms before the WiFi becomes active). The watch has no way to present this login webpage, so it connects to the WiFi network, but can’t actually access the internet. The workaround is to use your phone to forget that WiFi network (while the phone is connected to the watch). Since it will no longer be a known network then the watch will no longer attempt to connect to it.
Of course if you are one of the many people who typically doesn’t connect to public WiFi networks with interstitial logins then you won’t run into this problem at all.