It appears that AMDquickstream was conflicting with Avast Internet Security.
I have uninstalled AMDquickstream, and now the beta Avast Internet Security has no apparent issues when browsing various websites.
The rest is this post is just more details, just in case you are interested.
AMDquickstream is installed on some laptop and desktop machines that have AMD hardware. The software is a end-to-end Internet traffic shaper, giving priority to packets of high-priority tasks. It is suppose to help when there is congestion. As far as I can tell, for those of us with decent Internet connections (my.xfinity.com "services" page says my plan is 105Mbps down, 10Mbps up, but actual measurements are 240-250Mbps down, 12Mbps up when using speedtest.xfinity.com and www.speedtest.net) don't need AMDquickstream. Besides, I don't play Internet-intensive interactive games; the most intensive Internet use (besides Speedtest) is playing a YouTube video or playing a Netflix stream.
I don't know if AMDquickstream was initially installed by the computer manufacturer or if it got dragged in with another package I downloaded from AMD.
I discovered AMDquickstream by looking at the processes in the Windows Task Manager and Googling those I didn't recognize, and AMDquickstream was near the top, and the description of it dealing with packet prioritization sounded like a good candidate for causing Avast to lose what application a packet was for/from. It was probably just a few packets until Avast 17.3.2290 came along and then the two bumping heads caused a lot of packets to be blocked.
In any case, I used Control Panel -> Programs / Remove program to remove AMDquickstream, rebooted, uninstalled the ISP's antivirus package, installed the beta Avast Internet Security package (beta was what tech support had suggested), turned on firewall logging of blocked packets, another reboot, and started testing.
So far, after Avast has finished starting up, I haven't seen any blocked packets, not even to hxxps://bugzilla.mozilla.org/show_bug.cgi?id=1337246 and my system seems to be behaving like it should: the sites I expect to come up come up fine, no video streaming issues, and after a few more tests that in the past had anomalies (such as dabplayer audio streams not always loading), I'll update the ticket I had opened with Avast Technical Support and let them know the resolution. Update: after some more testing, I have updated my support ticket and expect Tech Support to close the ticket tonight (my time) / tomorrow (their time).