How do radio altimeter systems compensate for objects on the ground?
Objects on the ground are negligible because the radio altimeter is not designed nor used to such high precision.

There are several uses of the radio altimeter. The first one is for timing the flare during the last portion of the landing. Since the flare maneuver starts after the aircraft has crossed the runway threshold, at this time the aircraft is over flat ground.

The second usage is terrain awareness. The radio altimeter will trigger the GPWS "terrain! terrain! PULL UP" warning if the reading is too low. If you are in a range where the height of cars or trees matters, you are too low anyway.

You may imagine that pilots use the radio altimeter as their main data source for height above ground during the landing phase. That is not true - the barometric altimeter is always the primary instrument to use, until the flare portion at least. That is why pilots need to adjust the altimeter to the local air pressure setting. However, the radio altimeter can provide useful situation awareness. For example, you are landing at an airport with elevation 2,200 feet, you are 10 miles from the runway, and your altimeter reading is 3,800 feet. Suddenly you hear the automated voice "five hundred" in your cockpit. Needless to say something is wrong.

Pilots cross check the barometric altimeter with the radio altimeter during landing. The airport elevation is usually dialed-in somewhere on the cockpit display for quick lookup. When the automated "five hundred" announcement is made (or announced by the pilot not flying / flight engineer on an aircraft without automated announcement system), you quickly glance at the barometric altimeter to see it is 500 feet above airport elevation. It does not have to be exactly 500 - 492 or 518 will do as well. Then you cross check the distance to runway threshold with the DME (if available). Again, you don't have to be exactly 0.8 nautical miles or whatever distance the calculator come up with. As long as you're reasonably close, it is good enough.

If the pilots are using the ILS, then vertical guidance will be provided by the glideslope signal until decision height, at which point they will switch to the barometric altimeter again.