Not sure if serious or trolling, but I think it's an interesting topic and I haven't had a chance to write any multiparagraph pseudo-essays since I stopped hanging around Crunchyroll's forums, so I'm gonna indulge myself. (Woo!)
(As a disclaimer, I'm not necessarily attributing the point of view of the picture with AsianGuy. I'm honestly not super clear if this is sarcastic or sincerely agreeing with it. I don't want you to think I'm jumping down your throat on this because internet outrage blah blah, but conversely, if you - or anyone here - does agree with the sentiment on the picture, it could make for a fun discussion!)
(Edit for second disclaimer: I didn't click the link because I've been trained not to trust those when they're put up here in random new threads by people who just joined, so this is purely a reaction to the image. Sorry if the page in question provides more context - paranoia won out.)
I've got two main points here. First, people cosplay for different reasons, and while I don't think there's anything wrong with appreciating cosplay that's particularly true to the source (because of course there isn't - that takes skill and effort to pull off even IF you've got the right body for it), that's not the only "point" to cosplay. Plenty of people just want to express that they like or relate to a certain character, or use it as a way to start conversations with fellow fans, or just want to wear something out of the ordinary. I don't think any of those are wrong ways to participate in cosplay, and none of them demand that the portrayal be as accurate as possible. If you like being a purist, cool. Compliment those cosplayers who you feel have done a great job portraying their character. But it's shortsighted to assume that everyone in cosplay is doing it with that as their goal, and going around telling people their facial structure isn't similar enough is gonna get you some weird looks.
Second, anime is abstraction, and abstraction is a powerful thing. Ignoring the (rather large, actually) stylistic variations across anime, anime characters all look like anime characters regardless of the setting they appear in. A Japanese character in an anime set in Japan will look the same as a Western character in an anime set in the west, will look the same as a character of the point-of-view culture in an anime set in a completely fictional world. Filtering a character through abstraction is a great way to make that character appeal more broadly - the audience by default isn't given some of the cosmetic information that might alienate them. Animation has the unique advantage over live-action of being able to present a character without a race if it wants to, and ignore that potential hurdle in a viewer's association with the characters. Departures from that style can even be used to give visual cues as to how race is perceived from the point of view of the protagonist, even in such a way that circumvents the viewer's own real-life perspective. Many anime set in Japan have western characters drawn in a different style, but the same is true vice-versa. You could feasibly set an anime in Africa, use the default anime style for the protagonists, and portray characters from regions further north with literal white skin, and it would still make sense. Attributing a single race to the anime style isn't reasonable when there are plenty of counterexamples right there in the medium. Anime is race-fluid: ethnic depiction is entirely up to the particular anime. The same rule (specifically, the lack of any universal rule) ought to extend to cosplay too.
Also racism and overall meanness, but I think that argument more or less speaks for itself.
tl;dr Nah. Don't ruin cosplay for people.