While OS X is inherently much more secure than the-operating-system-that-shall-not-be-named, the only truly invulnerable computer is one that is BOTH air-gapped (not connected to anything else) AND completely shut down. Viruses that target the Mac platform are relatively rare at the moment, and they're generally not able to do as much damage for now, but both of those circumstances are beginning to change as Apple's market share continues to increase.
If you're very disciplined in your browsing and e-mail habits, your Mac can (probably) survive a bit longer without protection, but the time is rapidly approaching when a really good suite of security software is just as necessary on OS X as it is elsewhere. I personally believe that time has already come, so I'm continuing to run Avast for now. If that product proves to be a major player in the mail issue and I end up having to ditch it, I'll be running another product immediately.
And for whatever it's worth, I continue to maintain that, while Avast might be making the problem worse on some of the systems that are running it, I don't believe it's the actual root cause of the issue. My system and my wife's are both running fine with Avast up and fully operational (including Mail Shield), and there are several folks on this thread who are continuing to have problems with Mail, even though they've never installed Avast.