It's the urethane front swaybar bushings. Urethane doesn't "self lube" like rubber does, and is harder. With the smooth bar and the smooth urethane, you get the same effect as basketball shoes (or skin) on a gym floor - squeek (and "ouch").
Only solution is to rough 'em up a little inside (wire brush) and lubricate. Most recommend a silicone grease (not spray) which is more friendly to urethane, though some have had success with lithium grease. I'm going to try to get some Krytox, a very slippery DuPont lube that doesn't wash off (do NOT get it on your hands), but I'm not playing around under my car at 20 degrees, so the first visit may be to the dealer to get the squeak temporarily eradicated under warranty.
Good news is that while it sounds like hell, it's not doing any damage, except to your reputation (and Mazda's) if you have guests in the car who wonder why it's falling apart (it's not). Tell them it's the racing suspension and on the track it doesn't make any noise at all. You don't have to race to say this.
In short - dealer for warranty visit, and if you can get them to Krytox it, so much the better. If not, well, you'll go back when the lube wears off.
Good luck!
(now WHY am I continually posting AFTER girth?)
You pretty much gave all the needed info in 1 post anyway so all others are irrelevant.
