I'll be addressing comments from a few people.
First, I agree that the reaction was probably more due to the fact that you were eating the carrots around other people (in public?). There is also the "noise" factor. Eating raw carrots is not a very quiet business. It attracts attention, and attracting attention is not usually a good thing in Japan. Also, even in the USA, most people (from my experience) do at least cut carrots into pieces before eating them. Eating a whole raw carrot in public would probably conjure up images of Bugs Bunny.
It seems that the use of "night soil" is no longer common in Japan:
"Actually, only 1% of human excreta is utilized to farmland at present and the rest is treated by advanced night-soil treatment systems."
公益財団法人 国際エメックスセンター
Anyway, considering the various things that are usually sprayed on fresh produce these days, I peel things with any sort of skin. In theory, the skin of an apple, for instance, is edible, but in practice, apples are nearly always sprayed with wax and who knows what else, so I
always peel apples. Carrots don't have so much of a skin, but they do come from the ground, and if I did not peel them, I would thoroughly scrub them with a brush, so I figure I might as well peel them.