This morning, I once again tried to click on a different tab with a Google Calendar reminder open in Chrome. And I'm not alone, many people have been confused by the fact that these pop-ups act like Windows modal dialogs. In other words, you can't do anything in Chrome until you dismiss the reminder. Fortunately, things are changing. Google has announced that a feature in their labs is now available to anyone.
They are calling the new native browser notifications "gentle reminders" which is a pretty good name considering how abrupt the old version can seem. If you enable this new feature, you'll be able to ignore a calendar reminder and freely click around Chrome (as you can see in their animation, you can also write emails, etc). Some people would prefer to not have that freedom--I'm still on the fence.
From the gentle reminders announcement, "This new feature is opt-in and automatically activated for existing lab users. In order to opt-in, simply enable browser notifications from the settings menu in Google Calendar."