Avast! for Mac is generally known for not requiring any user intervention, you install it and if you stick to the defaults you don’t have to worry about it.
But like on PCs there are exotic cases of conflicts between apps, Mackeeper is also an antivirus and internet filter, and apparently wasn’t completely/correctly uninstalled from your system (it likely installed components elsewhere and only the app in Applications was removed), there might be a conflict between the two apps.

In such cases of incomplete uninstall, I reinstall the offending app, follow the procedures the vendor recommends for uninstallation (they probably have an uninstall app or mechanism inside the app).

Mackeeper uninstall procedure for the current version: http://help.mackeeper.zeobit.com/Manual/GettingStarted/UninstallingMacKeeper.html

Earlier versions: http://applehelpwriter.com/2011/09/21/how-to-uninstall-mackeeper-malware/

Apparently Mackeeper developers didn’t make it easy to uninstall their software in earlier versions, shame on them.

Until that is resolved Webrep doesn’t matter.