There are a few reasons why we can't see green stars:
- stars are not naturally green
- the atmosphere acts to 'redden' stars
- human vision doesn't normally see color at night
Stars have a natural color, based on their temperature, size, and life-cycle. The hottest stars are blue, while the coldest stars are a red-brown. That is, no stars are naturally green.
Secondly, both the Earth's atmosphere, and the space between Earth and any star, contains dust particles. The way light is absorbed and bent by these particles acts to 'redden' the ray. So stars that are intrinsically orange will look more red for an observer on Earth.
Finally, a reason is the make up of our own eyes. The sensors in our eyes are called 'rods' and 'cones'. These two types of sensors have different roles, but it is the cones that 'see' color. Cones need a lot of incident light to work, so they are not very effective at night - therefore, our vision is mostly greyscale at night. Furthermore, we perceive stars as point sources of light. It is unusual to be able to define a color for a single point. You may be able to discern some color for planets or nearby stars, but without the use of a magnifying instrument (i.e. telescope) the naked human eye sees most stars as grey-white.