Having a reputation as smelly and unwashed can have a very negative effect on one's life and livelihood, too — but if someone points out that you smell bad, you are better served to update on that (and take a shower) rather than responding as if it is a slur.

Depends, if people frequently used accusations of smelliness as universal counter-arguments, they way they use accusations of offensiveness, it would make sense to question accusations of smelliness.