I have a few acquaintances who are from different places in south east Asia. As far as I can tell it's the same for them as for me. I think the main problems happen when you look close enough to ethnic Japanese that you
might be Japanese. If you pair that with flawless Japanese language skill, then people will assume you are Japanese. This caused a problem for a friend of mine who was Korean, but spoke Japanese without an accent. Sometimes his acceptance of the culture didn't match the expectations placed on him. But I suppose it's hard to complain -- people treating you exactly as they would treat anybody else.
Another acquaintance is dark skinned (I can't remember where he's from) and has similar Japanese ability. I think he's has a softer landing. Even I get it pretty easy sometimes and my Japanese ability (both language and culture) is pretty middling. There is a kind of role in society where you can be the "friendly gaikokujin". Everybody wants to talk to you and learn about foreign places. They want to know how cultures are different in other places. If they feel like they can treat you as a Japanese person, you get a kind of celebrity treatment. I think this is probably only the case in the country side, where I live. In the big cities, they see enough foreigners that it isn't so special.
Most problems I've seen come from people using their "Super Gaijin Powers" (can't remember where I heard that first -- I didn't make it up). Basically if you look different, you can often ignore societal rules with no apparent penalty. You do whatever you want. You dress however you want. You say whatever you want. Nobody will complain. But there are huge unseen penalties and when those penalties become apparent, people get very angry.
A good example of this that I saw often when I was working as an assistant language teacher at the high school was foreigners not going to work parties. At the end of special events (and randomly through the year) there are parties where you go and eat and drink (often a lot). Some of my colleagues just refused to go because they said that they couldn't speak to anyone, didn't drink, didn't like the food, it was too expensive, etc, etc. I would tell them, "You have to go. If you don't go, you won't get along with anyone." They would reply, "Nobody cares if I go. I just tell them I'm not going and nobody says a thing." One or two years later: "Everybody is so unfriendly. Nobody talks to me. They all avoid me. They never listen to my ideas. They pretend that they don't speak English, even though I know they do. They are all two faced bastards. I can't wait to get out of here". It's so frustratingly predictable...
But, anyway to the point: If you look Japanese enough and speak Japanese well, then you probably won't get away with abusing your gaijin super powers -- so in the long run it might be easier. Even for me, I had bit of a health problem and had to cut out drinking for a few months. It happened to coincide with drinking event -- which I attended but where I drank tea. One of the other teachers was so upset that he lodged a formal complaint against me (it's on my permanent record!) I later apologised profusely and went out drinking with him and we were the best of friends after that. There is no way that he would have complained if he didn't consider me "close enough" to Japanese.