I was having this same problem. I first noticed it when I went to my bank site. The switch banner came up, and problem was, IF I switched to safe zone, I then could not go anywhere within the Safe Zone browser -- nothing but a blank page no matter what (Google.com, Avast.com, any site). Then it (the switch banner) started nagging me everywhere.
Not sure if this will work for everyone, and I admit I'm not that geeky a gal, but I finally figured out a solution that is working for me. (It did not, by the way, solve the problem for me to change the settings in the Avast program directly, under tools > Safe Zone).
What finally did it for me was -- and this is in Firefox (latest browser update, 26.0) -- to open the Avast Online Security Settings from the browser (it's a green circle-y sort of icon on the main toolbar). I clicked on that, and at the bottom, went to "settings," and from there, I unchecked the "SafeZone" box.
Just throwing that out there in case it helps someone. Like I said, this is what finally did the trick for me.
UPDATE: I apologize. I thought that took care of things, but the box keeps getting re-checked, sooner or later, no matter how often you uncheck and save settings from the browser thing.
So... *finally* finally (let's hope) I just disabled the Avast Online Security extension (Firefox toolbar > Tools > Add-ons > Extensions). If it returns at this point, then Avast is haunting my Firefox browser. lol (By the way, I was able, throughout this, to go to my banking site with no problem via Chrome; didn't try IE.)
This extra bit of security would be terrific IF it actually only arose when accessing sites such as banking, PayPal, shopping sites, and such. And then, it would be terrific IF it would then actually allow you to actually access said sites instead of a blank browser window (which pretty much defeats its purpose, I'd say.)