Just skimming over their code, basically what Yahoo does is to encrypt your information before sending it if you have javascript enabled. That way, if someone were to be sniffing the traffic to and from your machine, it would be a whole lot harder for them to get your username/password. If you don't have javascript, it will just send it plain text.
This kind of javascript is pretty rare, though, and usually isn't what sets Opera off - most of the time sites will have javascript to make sure that you didn't leave your password blank. In this case also, it doesn't matter if you hit yes or no, you will still let you pass.
In fact, if you ever find a site that doesn't let you pass if you hit the "no", I would be very concerned about the site's design and security. You should really never depend on javascript like that.
