Sometimes I do, sometimes I don't. Going out for a 1000 foot mooch around in the Cub or Moth, I don't find the absence of a parachute troubling, nor do I in a PA-28, which I don't think would be at all easy to get out of in an emergency, even if the seat could accommodate me and a parachute.
Don't feel bothered flying the Firefly around gently without a parachute, but I'm not going to spin it without out. If I'm flying the Yak I always wear a parachute these days. And in anything without a PA-28 style saloon-car interior (Cub, Moth, Yak, Firefly etc) I do also wear a proper flying suit and a bone dome. Perhaps I should in the PA-28 as well, perhaps I'm being inconsistent.
I think Yakker makes a very good point about passenger briefings needing to include the use of the parachute, and the instructions you will give. This is what you get when you fly in a military aeroplane, and it does mean you need to spend longer working on the briefing and delivering it. Pax briefings for the non-type-experienced have to be a lot more thorough for tandem cockpits in any case, as you can't necessarily help the other person in-flight, or see what they're doing. For example, I always make a passenger new to the Yak practice opening and closing the canopy to its various settings while I'm watching, just so that we both know they can do it properly.