In an ideal world, Korean fans and international fans would get along perfectly well, respect each other and not even categorize each other as 'K-fans' and 'i-fans' but just simply as 'fans'. Sadly, we don't live in an ideal world, and i-fans and K-fans clash all the time. Now, before I continue, I know not everyone is like this and I'm just viewing this from a more broad overhead perspective.
When I check Korean news or blog sites and read some of the comments and posts, some of the commentators seem to look down on i-fans. But that's not to say that the condescension is just a one way street. When I look through Tumblr and Twitter, I see just as much i-fans, if not more, hating on K-fans.
A recent event I remember happening is when a certain international EXO fan went to Korea and filmed EXO fans. In the video (not the original which was taken down), she was told by a Korean fan (you can barely hear it above the crowd's noise), and then got slapped by a Korean fan in line because she didn't hear / understand what was being asked, and she didn't stop. It was a clash between two people, not between two nationalities, but the comments on the YouTube video quickly made it into a battle between two races. I saw Korean comments claiming that they felt like they were animals in a zoo because a foreigner was filming them, when it clearly had to do more with what goes on in a fandom, not what goes on in a country.
After that, the most recent clash I saw happening is the stance of different groups on Super Junior-M members. At first, I didn't really consider it a difference between i-fans and K-fans, until I started looking through posts on Korean blogs that claimed only i-fans said to accept Zhoumi and Henry as 'full' Super Junior members, but that they had no right to claim any of these things because they're just i-fans and they don't buy anything.
This personally offended me because for full disclosure, I own pretty much every single official merchandise Super Junior has ever put out. I might sound like a crazy fangirl, but I have different versions of the same album and then buy the repackage (and its different versions) when that comes out. On top of that, I have a Bugs account and I legitimately buy all the music, so I buy the same album 3-4 (sometimes even more) times over. It's not just albums, but just all official merchandise. Perhaps I'm an outlier, but to be told that I'm not allowed to have opinions on how my favorite group does because I don't buy anything... well, that made me a little upset, but it also made me realize that the rift between i-fans and K-fans can sometimes be bigger than I thought it would be.
Why does this rift exist? Mostly it's because of the cultural differences. What most Koreans see as obvious doesn't seem too obvious to i-fans, and what a lot of Korean fans see as a big deal doesn't seem like a big deal at all to i-fans. One of the points that Korean and international fans clash the most on is the topic of being conservative, with Koreans saying some clothes are too short and too revealing while to Western fans, it's something they see on a daily basis in Western media.
Another point that's hard to understand for i-fans is the topic of army enlistment. Risking running off topic, I'm going to take this time to explain why enlistment is necessary, at least at its most basics. Korea's had mandatory service since January 1950, after Korea was divided into North and South. Mandatory enlistment is not as rare as a lot of Americans think it is - actually, our next-door-neighbor Mexico also has mandatory enlistment. Although it's a bit different from the conscription in Korea, it's kind of a necessity for countries under some form of threat to have it. In Mexico's case, the 'threat' is sharing a wide border with the United States. Taiwan also has one since their independence from China. Korea's threat? None other than North Korea.
In fact, enlistment is a huge deal in Korea. Enlistment can have a huge impact in Korea, and the person who felt the biggest impact is none other than Yoo Seung Jun, who was at the height of his career when he fled to USA and then to China. He's pretty much hated all across Korea. While it's true that enlistment can also have positive effects in the case of Hyun Bin or Yoo Seung Ho, a lot of i-fans hate it when their idols go to the army because it means 20 plus months of not seeing their favorite stars.
Of course, it goes in the other direction, too, and the biggest example I can think of is the terrible instances of blackface. Perhaps because they don't really know the history behind how offensive it is, some Koreans find such skits to be funny. Comedians do it. Yesung and Kikwang have done it, and most recently, 'Running Man' also featured blackface. The idea is simply ludicrous to i-fans, but to some K-fans it's not racially offensive at all. Perhaps, due to lack of exposure to the negativity?
A lot of it is also because some K-fans don't like 'sharing' their idols with international fans. Korea
can be incredibly possessive of their artists and also a bit xenophobic (like every country is), and they're immediately wary of fans from the outside. Their hesitation against i-fans is kind of paradoxical, because they all boast about how big their group's international fandom is, and how big of a Hallyu star they are - and yet they don't actually like the i-fans, the actual force behind Hallyu. If you really want it to be a popular cultural export, let it spread. The farthest they'll go into admitting i-fans is only for Japanese and Chinese fans, and they scoff at pretty much outside of this.
One problem is that Korean labels have a tendency to sometimes look at 'Asia' as the 'world'. Most of the time, artists go on Asia tours (these used to be called World Tours until artists started to branch out into the Americas, Australia, and Europe). So if the labels see Korea-Japan-China as pretty much the whole world, the K-fans don't really have a reason to see other countries' fans as "real" fans.
Of course, that's not to say that all i-fans and K-fans are at each other's throats all the time. In my own fangirling experience, I've met various k-fans who were more than happy to help out i-fans get some merchandise that was only available in Korea, or help i-fans make sure their gifts are sent out to idols.
What would be nice is if all K-fans could recognize that i-fans love their artists just as much as they do. In the end, what both K-fans and i-fans need is better understanding of each other. I understand that's much easier said than done, but I'm optimistic and here's hoping we can all get along.