I learned that the idea that foreigners stink came from when the Dutch first came to Japan, after sailing for god knows how many months, unbathed and eating beef, something Japanese didn't eat, they had a smell. I can imagine this would have largely been the case even 100 years ago regarding every Western country. Even today. In Japan old men might smell like beer, cigarettes, or B.O. An old, unclean fat guy in the States, however, could make you gag. Plus we still eat more greasy, unhealthy food that causes an odor to emit through our pores. Different physiology as well, but I'm not sure how much of a factor that would be.
As far as deodorant, yeah, just get it. The aluminum-ion containing anti-perspirants are what I used. The aluminum is not good for your body long-term, however, so in winter or inactive days I've turned to using something that prohibits bacteria growth only, thus reducing smell. Tea tree oil, lemon oil, coconut oil...Gold Bond powder has menthol which works. There's a healthy Gold Bond that uses vitamin E, aloe, lavender, etc. to slow bacteria growth. And the powder absorbs moisture. Nothing works like anti-perspirant though.