I certainly don't think that it's mostly people who are Caucasian who are making jokes about people who are Asian, that my friend is a racist remark in and of itself.
In some Asian countries, many people have plastic surgery to remove their Epicanthic fold, and to remove some of the material in the eyelid. As well, Asian people are not the only people who have an Epicanthic fold. I am not Asian myself, and yet I have an Epicanthic fold.
No matter your race or ethnicity, skin color, country of origin, nationality there will always be others who will find humor, racist and not in who you are. Caucasians, people of African decent, Asians, East Asians, South Americans, Slavic, Middle Eastern and so on and so on.
You can either choose to be butthurt, you can ignore it, or you can choose to see humor in whatever it is that is being said. Personally, the world is a far better place when you choose to either ignore that type of thing, or see the humor in it if in the form of humor. If it's blatant racism then you can always respond, or as the Native North Americans practiced with their children when they displayed behavior they did not wish to promote, nor did they condone they would ignore the person as if they did not exist.
What I don't feel is right, is to say one race is more prejudiced than another, no matter the race. You cannot possibly know this unless you can cite research that was done on this subject.
You might find this map of the world, and the study that was done that specifically relates to racism interesting:
http://www.dailymail.co.uk/news/article-2325502/Map-shows-worlds-racist-countries-answers-surprise-you.html
If you look at that map, the top countries in the world, that score the lowest on racism happen to also be countries more populated by Caucasians. That is a fact, and I just cited it. You might try the same when posting things of an inflammatory nature.