Hi there,
I am having the same issue. In the last couple of weeks, Chrome and Safari on my iMac and Macbook (each in different location – office vs home) are randomly giving me err_connection_reset for random websites, sometimes it lasts for 30 seconds, sometimes for several minutes. It is very annoying and it starts to affect my work.
I tried all the usual "reset everything", update all OS etc etc etc. I have even discussed this issue with my ISP who advised couple of things to try like testing various DNS (cloudflare, google etc.), but nothing helped. Until...surprise...I switched off Avast Web Shield and the problem went away (so far).
I don't feel comfortable to have WebShield switched off, but I need to work as well. If it is Avast-related problem (and so far everything seems that is is), it would be really nice to have a fix asap.