Auto lockers - Lock-right, Detroit, ect. can be used on the street, but they create interesting handling traits that not everyone is o.k. with. Lets look at what they actually do rather than just pissing back and forth uhhuh, nahuh.
Throttle off, one side can walk over the other side, so if you're in a corner with the throttle off it doesn't do anything spooky other than you might hear it ratcheting.
If however you apply the throttle midway through a turn, the locker will engage (lock) and you've gone from two tires spining at different speeds to two being forced to go the same speed. This can make for some interesting handling and is why many people say not to use them on the street. It is definately different, especially if you're not ready. Different lockers are more abrupt than others - that's why detroit came out with the 'soft locker' at one point. Different vehicles react differently too depending on tires, suspension, weight ditribution, wheel base, ect. A CJ-5 with 6" lift and 38's is going to react alot differently to a locker locking up in the middle of a corner than a F-350 Crew Cab Long Bed on 32's.
This can also screw you up off road. You're already in a big van so your turning radius isn't that of a samurai. Throw a locker in there that you can't turn off and it's going to want to push straight whenever you're on the throttle. I think this is worse w/ 2wd cause you don't have the front pulling you around. In loose stuff on the throttle it'll also make the rear end try to come around. Rallycrossed a friend's D50 w/ a spool and compared to the tacoma w/ open rear I had the tail was way wilder on his truck. The advantage of course was in corners I was spinging my inner rear and loosing momentum (which was actually probably saving me from flipping
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).
The snow ice comment is the same type of deal. Some people will say it's o.k., but opinions vary. What happens, and this happens even with posi (LSD) to a degree (more when it's a 70's El Camino w/ light rear end) - is one tire is on ice and one tire on dry pavement the truck spins. It's very close to using a turning / cutting brake cause you have one wheel doing nothing, and one pushing forward twisting the truck/car - either toward oncoming traffic or toward the ditch. Normal open differentials won't do this. This isn't as bad with 4wd as it is with 2wd, as you have a front tire pulling and helping keep it from rotating.
Myself, I'd take a selectable locker over any other choice (I just happen to have two of them from the factory on my LX). If I couldn't afford that, I'd go LSD or a winch. For me it's not that a auto-locker would be undrivable on the street, it's that I have run into situatutions where I have to loan out my truck, like to my mother-in-law - and I don't want to have to worry about how she's going to react to it being different.