Why do some women get bothered when another woman wears the same dress?

It is interesting - they do get bothered. I suppose it has something to do with 1) not being "original" (what we wear is supposed to be a sign of our uniqueness), 2) the clothes not been "tailor made" - off the rack, so to speak (which in modern times is how most of us buy our clothes - but originally mass produced clothes, were for the "masses") and 3) because it encourages comparison (who is wearing it better). The fact that it doesn't bother you reveals to me that you are confident, and not too worried about what other people think. Good for you.