The stickiness results from the plastic/rubber degrading due to temperature, UV exposure, or even some oils and greases. There are some home remedies that seem to work pretty well:
1.) Use some alcohol-based hand sanitizer or sanitizing wipes; gently test on the rubber surface to remove the stickiness
2.) Use some baking soda mixed in water (make a paste) on a cloth; gently test on the rubber
3.) Use WD-40 on a cloth; gently test on the rubber
Some of these work, some don't...depending upon the plastic/rubber. Make sure to air dry any of these applications before using.