Absolutely. One of my best friends - though we've yet to meet, face to face - and I almost got kicked off a website, once, over the "Dear" thing.
Fortunately, we (eventually) talked through our issues (that was only one, stemming from another), and became friends. Pretty sure if she reads this at all, she'll "out" herself and say, "NEVER CALL HER DEAR, NOT IF YOU VALUE YOUR LIFE!" though we've been friends for almost 20 years now (OMG). She called me her "dear friend Holly" the other day (not the same thing at all!) and apologized - knowing, I'm sure, that I was laughing as I accepted it. But you have to establish grounds, with me, for such endearments. And it IS a cultural thing - I live in the south, where it tends to be a universal term of endearment. I grew up in the more reserved north, where you just don't presume that level of affection.
To be fair, I know many women who are offended by being called "Ma'am," but if it's the implication that they're older, I'm happy to own every gray hair I've earned.