I think it depends on the person. Some pride themselves on being a dyke while others don't like it so much. I know lesbians that call themselves dykes and other that only date dykes. To me it is a subculture of a sexuality used to be describe what someone is or looking for. I always thought it was a a synonym for 'butch', you know the more masculine of the lesbians. However, I can see it being offensive if used in a certain context especially by a non lesbian or stranger. I think it's like the 'n word' if you are African and say it with an 'a' it's ok, but otherwise it is a dirty word. I personally would never refer to anyone as either out of respect, so yes I would be offended if I were you, unless that is what you were going for.
I would consider that word to be offensive and insulting.
Yes it's rude
dykes good in Holland...
no, but someone women find it offensive