Why stars are white? According to Rayleigh Scattering According to Rayleigh Scattering, the red waves are capable of travelling a long distance, so that only we are seeing the Sun as reddish during Sunset and Sunrise.  If this was true then all other stars must also appear red in colour, as the distance through the atmosphere travelled by those lights is further during sunset or sunrise.
Why do stars still appear white?
 A: The colour of stars as observed by an observer on Earth varies just like the colour of our own Sun, depending on where in the sky the source is relative to the observer.
However, the light of stars is generally too faint to notice this as clearly with the naked eye, because we cannot perceive colour for weak light sources.
A: No,  Rayleigh scattering models the probability (and angle) of scattering as a function of wavelength and of the particle sizes. All wavelengths travel a long way but the path followed (scatter or nonscatter) varies. 
Since space is mostly "empty", there's little scattering.
Beyond that, your understanding of stars is quite incomplete.  THey do in fact have a variety of "colors," aka peak lambda outputs, depending on size, age, etc.
"White," as a color, is a perceived effect and can occur either when a bunch of wavelengths hit the retina simultaneously OR when the input intensity is extremely high.  Then there's a third case: in very dim light (e.g. most stars during a very dark night), our color receptors don't respond and only the 'grayscale' cones in the retina respond.
A: *

*Starlight, as emitted by a star, comes in a wide range of colours. For instance see the picture below. 
Now this is a picture, and pictures can often be tricky with their representation of colour, so you'll have to take my word for it that Betelgeuse does look significantly redder to the naked eye than say Vega until you get a chance to go look yourself on a dark clear night. 

*Contrary to what some of the other answers are saying, scattering in space can be substantial. In the context of this question, Mie scattering is probably the most relevant process (Rayleigh scattering is a special case of Mie scattering). Mie scattering causes interstellar reddening - stars that have a lot of dust along the line of sight appear redder than they would in the absence of dust.

*Rayleigh scattering in the Earth's atmosphere affects starlight the same as sunlight (the light incident at the top of the atmosphere may be redder or bluer than sunlight, but it will be redder by the time it gets to the ground, just like sunlight).

*Finally, as others have mentioned, human eyes operating in low light are bad at seeing colours, but alright at seeing variations in intensity, so faint stars may appear whiter than they otherwise should to a human eye ("cones" need higher intensities to work than "rods").

