Hey there, I know this post is old and dated and all, but I've too been experiencing this same issue every time I boot up my computer, being prompted for "private/public" connections preferences. I use a VPN as well so I understand if it asks me often. I am connected via hardwired connection (Ethernet) not wireless, too. I have owned the Premium version of Avast for some time now.
I wish I had noticed this post sooner. Is is closed?