Though maybe not on the same level, many non black people deal with the good hair/bad hair issue as well. Its just not talked about as much IMO. There are several threads on this site that discuss women of various ethnicities having to deal with it. One example would be the "Case of Mistaken Race" thread on the 3C board.
I don't think white people care as much about what black people do to their hair in general. However, in terms of the standard of beauty- i.e. black women's hair in its natural state deemed unacceptable- I think this is perpetuated a lot by white people as well, its just done more quietly.
There is a tremendous amount of self hate that encourages black women to straighten/perm. White women with curly hair are under pressure as well but not at the same level. While many white women are born with straight hair, much less black women are. So when black women are pressured to straighten, it is a larger issue. They are being pressured to change something that is generally seen as a phenotype of another ethnic group. Society sends the message that straight is better than curly and curly is better than kinky. Looser textures are seen as more acceptable. However, afro textured hair is looked down upon in any texture.
Hair that is closer to straight is closer to a "white standard of beauty". Since most black women have wavy, curly or kinky hair, I would say this standard of beauty is race based. While there are white people with tightly coiled or kinky hair, it is much less common. It is so uncommon that many people don't even *believe* white people can have kinky hair!
Of course there are many ethnic groups that have naturally curly/kinky hair or almost always have straight hair, but in most cases, society tends to dice them up into "black" and "white" anyway. hence the black/white discussion. I don't see how we can talk about it without talking about race.