Were you using MacOS Catalina?
I tried checking "Open Avast Security when my computer starts up." It stayed checked after restart.
I tried removing/reinstalling Avast Security, and then unchecking "Allow usage data". Once again it was checked after restart.
By the way, I noticed that after the removal/reinstall, the Avast Online Security Chrome extension WAS NOT reinstalled. I had to reinstall it manually. I believe that previously the Avast Security installer had automatically done that. (It still has a step for Chrome Extension, but it didn't appear to actually work.)
Thanks.