I think that some Japanese have a certain image of what foreigners are all about and should do, and this may turn them off people trying to become 'Japanese' and may prevent 'gaijin' from fully integrating. Approaching Japanese culture in your own way is one thing, but trying to become Japanese is another thing. It's like a tiger trying to change its stripes, it seems unatural.
A few Japanese folks I've met were sometimes (completely unintentionally) blanketing in their remarks and thinking and I'm NOT by any means criticizing them, what I'm saying is that by contrast we politically correct and overly-sensitized Westerners with our high immigration influx levels and cultural exposure have distanced ourselves from some very basic stereotypes and half-truths that a culturally homogenous and low-immigration influx country may still have regarding foreigners.
I had a black friend from England who was told quite frankly that immigrants ran faster than native Englishmen and this was why England excelled in some sports. The guy was just trying to compliment him on his country's sports successes and meant no harm. In a press conference the president of Pride Fighting Championships told an African competitor that he'd love to have a Pride event in Africa, but only if he could watch this fighter fight a giraffe in the grasslands. Again, he was just trying to humour the fighter based on traditional stereotypes and what he knew of Africa.
There are more examples but, my point IS, I think some Japanese feel Japanese culture is definitely something for Japanese people and others should enjoy their own cultures with equal levels of enthusiasim. The two are very different. They find other cultures fascinating, there are more documentaries and travels shows on Japanese TV than you can shake a stick at, and outbound travel is a booming industry.
So for a gaijin to dabble and even get fairly far along in Japanese culture is something they applaud. However beyond this, the idea of a landed immigrant fully integrating linguistically, culturally, etc., and becoming Japanese when they're clearly not is strange to them, why abandon your own interesting and colourful culture and how can you hope to become Japanese in one lifetime? This is the essence of trying hard, anyone who's seemingly traded in their culture for another will seem strange. The idea of switching-over is something we're accustomed to in the West as many people aspire to live here, but this concept may still be odd to others.
Based on my experience, the ones who 'hurt' and try to hard, are usually Western-born. Here lies the difference. You don't see as many Indian, French, Turkish, African.. whatever.. Japanophiles as you do Western-born ones. Japanophilia seems to be a largely Western trend much like the strong Americanization of Japanese pop culture, its almost symbiotic. This may be because again, Western culture is consumer based and we don't really have cultural experiences of our own that are centuries and centuries old to cling to. Westerners are kind of the wine-tasters of world culture.
So within this arena what you may have is a group of mostly Western-born Japan-heads seeking out quick and complete cultural integration and on the other side Japanese people saying, hey, whats wrong with your own culture you can't seriously think you're Japanese, you're obviously 'this' or you're 'that'. From here theres a trickle down effect with varying levels of intensity.