I don't know how K9 works now, a very long time (many, many, years) since I used it, but it to must be acting as some sort of proxy to be able to filter content ?
If so there may be some sort of conflict between the two or it could be firewall blocking K9's changed processes, which may well be inadvertently blocking the web shield.
What is your firewall ?
Something you can try also, though I'm not sure of its benefit if previously K9 and avast were working ?, is:
- Try opening the avastUI, Real-Time Shields, Web Shield, Expert Settings, and check the 'Scan traffic from well-known browser processes only,' option.
As I said though if it worked with the 7.0.1426 version of avast before that shouldn't change anything, unless how K9 works has changed.