The anti-sway bar, or stabilizer bar, limits the amount of body sway and it a very important part for maintaining control of your vehicle. In turns, it keeps the weight centered over the wheels, so that it can maintain proper traction. If the weight shifts too much (like an emergency maneuvre) then you could wipe out or lose braking. So you should make it a priority to fix it asap.

I just helped a fellow co-worker do his CR-V stabiliser links, and it was fairly easy. I would say this is a job that a beginner could do in a few hours. The worst part was the rust (90's model), but once we broke the nuts free the rest went pretty quickly. Soak yours in penetrating oil ahead of time. Hint: the flex in the bar will hinder your effort to put torque on the nut, so use a piece of pipe or 2x4 to jam it.

He used "MOOG" parts, and they were built much better than the original parts. We could feel the difference in ride quality immediately.