At work, I don't generally recommend talking guns unless you know everybody at the office, or at least the ones who make the personnel decisions, are gun people. Some co-workers might complain about "hostile work environment;" some employers might decide to start random vehicle searches.
As far as converting anti's, I try that every so often. I usually try to mix factual and emotional arguments, as many anti's don't respond to facts alone.
I'll tell them about my cousin, whose German Shepherd scared off a guy who turned out to be a serial rapist, but who had conned his way into her house, and how her police department advised her to get a gun since she was about 20 minutes from their normal patrol routes.
I'll tell them about my best friend, who had to scare off three would-be carjackers.
I'll tell them about my ex-wife, who had a pair of stalkers follow her home while I was deployed. Our Rott-Shepherd held them at bay while she retrieved a Beretta 92 Brigadier.
I'll ask them what they would do if an intruder broke in. If they say they wouldn't shoot, even in self-defense, I'll ask if they have children, or pets. (Amazingly, there are people who might not shoot an attacker, but who would defend the Chihuahua...)
But I am not telling an anti that I carry.
And so far, none have noticed, that I know of.