Why does coconut oil freeze even in plastic containers.

A single plastic layer can insulate only for some time.
Keeping the same coconut oil in multiple layered bottle will keep the contents in liquid form much longer. There will be air layer between each plastic layer, and this is more efficient in keeping the heat in and the cold out. Trapped air is very good for insulation.

Keeping the same oil in Styrofoam container (which has more air trapped inside) will keep it liquid for longer time than a plastic bottle.

If you can trap air between layers, it will do a better job of insulating than without air spaces.

This principle works for other things too.
Hollow brick walls, false ceilings and double glass windows keep the cold out and the house cool or warm.
Multiple layers of clothing on a person than one thick layer keeps one warm much better.
A turban on the head helps in keeping a cool head in hot, sunny days.

The nature of plastic is to maintain the insulation process but its efficiency to keep the contents in the insulating medium detoriates with the time because of the close spaced binding molecules in the process of rolling while making plastics undergo changes causing the close spaced molecules to shift its original position and instead of remaining in the close shape, the molecules are haphazardly spaced thus allowing the air to penetrate inside the stored contents of liquid.
If the surrounding temperature is less than the melting point of the Coconut - oil, it would offer a favourable condition to freeze the Coconut - oil.
In case of plastic bottle freezing would proceed slowly because the same being densely packed.

The ability of transfer of heat through a medium depends upon its thermal conductivity. More the thermal conductivity the heat transfer will be quick. If thermal conductivity is less it takes more time for heat transfer. The unit of thermal conductivity is Watts per meter-Kelvin.

Plastic bottles are generally made of Polyethylene or polypropylene or polystyrene. They are bad conductor of heat and their thermal conductivities is in the range of 0.3 W/mK to 2.5 W/mK depending upon the mixing material in it. The traditional glass bottles which are also bad conductor of heat have a thermal conductivity of about 1 W/mK. As a comparison the steel or iron has a thermal conductivity in the range 30 to 70 W/mK.

So if we keep coconut oil in steel bowl, it will immediately solidify if temperature goes down but in plastic bottle it will take some time because of low thermal conductivity of the plastic material.

When we want to isolate an item from outside heat then we keep it in a container which does not allow heat to pass through it or even if it allows it allows it in a long time. For example tea kept in thermos does not get cool and remains hot for quite some time as the double insulated walls of the thermos do the trick. Same tea kept in an ordinary metallic container will get cool quickly. Plastic is a bad conductor of heat so the coconut oil will not solidify so quickly but after some time the outside temperature will affect it even through the badly conducting plastic wall. So it will solidify after some considerable time. I am assuming that the bottle is capped and if it is not capped it may solidify earlier as some direct heat transfer will take place from the open mouth of the bottle.

The plastic is a poor thermally conductive material. But not complete insulators. If we want to see that there is no solidification you have to insulate the plastic containers. Then they will be in melting condition only. Many times the temperatures in the night will be less than 20 degrees centigrade and the melting point if Coconut oil is around 24 degrees centigrade. If the temperature goes to less than 24 the oil will become solidified. Once it is solidified in a plastic container, because of the poor conductivity nature os plastic heat will not pass that past and it will not get liquified. Pure coconut will get freeze easily. If you made a little contamination it may not freeze easily.
If you keep in metallic containers like aluminium or steel containers, it will be easily get liquified. But there will not be any problem with the quality of the material because of solidification.