No, they cannot, Mig, sorry. That's the way the site's software works. There is no "setting" to be changed that would simply make it so. Otherwise, we would have to spend more money to have changes made to the site's software to accommodate your request. Would be nice, but the request would be low on the totem pole. (It would have to be written so that chapter threads only show up in the chapter members' lists.)
Notes for all: Those are not Alerts. The Alerts are found in the upper right hand corner. Those are threads created in those chapters. They post to the What's New list just like any other site activity (they/it's all part of What's New). Yes, you have to be a member of the chapter in order to post. Otherwise, if you are not not part of the chapter and/or interested in the conversation, just skim over it like you would any other thread you are not interested in reading, then when you've gone through the list of What's New, click on the Mark All As Read.