Do you remove the blue inserts on Kenmore electric water heater inlet valves?

These two nipples are called heat traps, when water is heated it expands and rises. These little flaps are to hold some of the heat in the water heater. You should use both of them. If you use copper pipe with solder joints you want to make sure and solder the 3/4 female adapter to a length of pipe and then let it cool before you screw it on to the silver nipples. Do not solder any fittings close to the nipples without using some kind of heat sink, a wet rag wrapped around the nipples will do the job.

The blue thing in the cold water side of the heater is called a "dip tube" it is there to carry the cold water entering the heater to the bottom of the heater and not mix at the top of the heater with the water that has already been heated.