I came across a post of an atheist page on facebook that stated that "varna means color, so varna might attribute to color based discrimination along side cast based discrimination" is that true?
Varna can mean color but has no connection with any discrimination. Varna can not be translated as caste either.
Vaisampayana said,’ Hearing these words of Arjuna, O chastiser of foes, Nakula of mighty arms and a broad chest, temperate in speech and possessed of great wisdom, with face whose colour then resembled that of copper, looked at the king ….’
Mahabharata Santi Parva Section Xii
Mahabharata says the following about Draupadi.
Yudhisthira answered the chief of the deities once more, saying, - ‘O conqueror of Daityas, I venture not to dwell anywhere, separated from them. I desire to go there where my brothers have gone. I wish to go there where that foremost of women, Draupadi, of ample proportions and darkish complexion and endued with great intelligence and righteous of conduct, has gone.’
Mahabharata Mahaprasthanika Parva Section III
Neither Nakula nor Draupadi were Shudras.