I use NoScript, but I don't allow googletagmanager.com to specifically run scripts on the my.avast.com. And I have no problem connecting.
There is no entry for googletagservices.com in my NoScript list, see image.
I don't use MVPS hosts, so it would only be NoScript blocking in my case and it isn't.
I never log out from my.avast.com.
Note: HOSTS file information, the 0.0.0.0 (a.k.a. 127.0.0.1 home) in the HOSTS file is essentially blocking those two, when any connection is attempted to the two domains the HOSTS file says look in the local IP Home and obviously it isn't there, thus blocked.