Removing the Rear Sway Bar WILL AFFECT HANDLING! Chrysler/AMC did NOT give up profits to put something on a car to do NOTHING AT ALL.
BUT, removing a rear sway bar may NOT affect handling in a negative way for the applications your probably considering.
Less roll rate in the rear increases under-steer, a desirable characteristic that is generally considered safer. There is less chance having an accident if you plow forward in too tight of a turn (under steer) than spin out (over steer).
Of course removing the rear sway bar will decrease over all roll resistance and make the vehicle lean more in turns and too much understeer is undiserable (you don't want to plow forward in easy turns, right?). I'd be surprised if removing that small of rear sway bar would do that. But, if you raising the vehicle, you've pretty much thrown balanced handling characteristics out the window.
Now, for the opposite, Removing Front Sway Bars that may reduce under steer and maybe even create over steer (depending on your suspension set-up) and many don't consider it safe, for speeds over 35 mph, unless you've totally re-done the suspension and done the math to make sure you have characteristics that make the vehicle safe handling at high speeds.