Is wearing perfume in public transports or rooms bad in Japan?

Japanese and East Asians don't get as much body odor because they have less apocrine sweat glands so they don't need as much perfume, cologne, etc.

From Wikipedia's article on Body odor:

East Asians (Chinese, Koreans, and Japanese) have fewer apocrine sweat glands compared to people of other descent, making East Asians less prone to body odor.

I don't really have too much of an issue myself as I grew up in North America, but my cousin who lives in Japan used to complain about foreigners wearing excessive fragrances.

I've lived in Japan for several years and this isn't my experience at all. It is quite common to encounter Japanese people with strong perfume, cigarette odours, halitosis, or body odours. Public transport is quite crowded and you will come into close contact with many people. Everyone becomes accustomed to their own smells and may be unaware of the discomfort that it causes others. As in every country, some individuals are more considerate of those around them than others.

One thing to note is that using deodorant or antiperspirant products is not a common cultural practice in Japan. It's not something many people do on a daily basis and these products have limited selection and availability in Japan as a result. Fragrances and perfumes are seen as for special occasions but people do wear them in evenings and on weekends. It's a pernicious myth that Japanese people don't get sweat or have body odour, it's common especially in onsen and the hot, humid summers.

I have not been to Japan yet, but I spent quite some time in a few cities in mainland China to share my perspective:

1. most locals did not wear perfume/deodorants in their daily commute, either when traveling by bus or metro;
2. most did not have strong body odor, but some did, especially those that spent hours laboring in more intense physical activities;
3. based on conversations I had with a few locals, it seems they do not use perfume/deodorants for the following reasons:
   1. they do not feel the need to use deodorants to counter their body odor;
   2. intense odors coming from a person are considered as something odd in daily life (whether they are pleasant or foul smells);
   3. perfumes are expensive products in their minds;
4. I ate local food in hundreds (if not thousands) of restaurants while in there and, despite the fact that Eastern Asians have less apocrine sweat glands under their armpits (as mLstudent33 detailed), I personally believe that diet has a significant impact due to meat, fish, onions and garlic (with high sulfur compounds, particularly when eaten raw) being consumed in lesser quantities than in the western world (for those curious enough, here's an article explaining diet relations to body odor). Of course there are several restaurants serving these in larger quantities but, from what I have seen, locals do not eat these dishes daily.
5. I am not East Asian myself and I personally stopped using deodorant while staying in there after a few months, since that even in hot "sweaty" days, my body odor was almost absent. In Kung Fu classes, my sweat did not seem to have an intense odor, at least none of the locals avoided training with me or commented about my smell (that I heard, that is :), but I did feel some of my classmates odors (none seemed to use perfurme or deodorants while training).