In May this year I purchased Avast Security Pro, with a two year subscription, and used it apparently without problems until upgrading to Catalina in November, after which I began to experience frequent but only occasional and from my perspective random problems with Safari, and other browsers. The live tab would without any pattern or apparent cause refuse to load a new page. Other tabs would appear to work, for a while, but no new tab could access the internet. Switching to another browser did not resolve the problem.
Frequently, though not always, the browsers would refuse to quit. Relaunching the browser after a force quit did not resolve the problem: the relaunched browser could not access the internet. Disconnecting from the internet and reconnecting did not resolve the problem.
At this point I would try to restart or shut down the Mac (MacBook Pro 15 inch, Mid 2014), but it would not restart or shutdown, hanging at some point after the Finder quit. The Finder could not be restarted, and it was necessary to use the power off button to close the Mac down for restart. This is of course not a pleasant experience.
On restart, which was slow, Avast would sometimes relaunch automatically and present its window, suggesting, I suppose, that it had been open at the time of the crash.
This very inconvenient problem recurred many times, several times a day, and after careful examination of the situation, and a process of elimination, I realised that Avast was not interacting well with Catalina. I don't presume to judge where the problem lies.
I switched off all shields in Avast, and the situation seemed to improve (the machine was stable for some hours). This was good, but rather than make a longer experiment I uninstalled Avast and resorted to another security product, which I have used now for two days without any problems whatsoever, a length of time during which I would have expected the browser/restart problem to have recurred two or three times at least had Avast been running.
When I read that Avast (or Apple) have resolved this problem I may reinstall Avast, but not before.