Sorry mchain, but i'll have to disagree. I've already established in the OP that disabling the firewall restores network access in Windows Sandbox (you have to restart the Sandbox). And since network profiles is part of the firewall ...you see where I'm going with this...
I'm not aware of any setting to disable the network profiling in avast. It looks integrated into the Avast firewall itself. Since this profiling issue reared its ugly head after the v1903 update, it stands to reason that Avast need to iron out the bugs in this module.
Edit: The attachment you uploaded says v18.8. Those settings dont exist in v19.6....unless i'm mistaken?
Edit2: After some hunting around i found an obscure setting called "Open old settings" located under MENU>SETTINGS>GENERAL>TROUBLESHOOTING. Hidden at the bottom is the "Open old Settings" option. Now you go to COMPONENTS>FIREWALL>CUSTOMISE. Here you'll see the NETWORK PROFILES settings.....phew! Finally, now were getting somewhere. So I untick "enable automatic profile switching". Close all the windows. Open all the windows to see if it stuck and drum roll.........still remains ticked.
It seems that us mere mortals have no power in resolving this.