See this is a larger problem - people get ****y about the swearing in DmC because they think the intention was to be "edgy" and some other bullshit.
It wasn't, it was an unmitigated look at the exact cultures being portrayed and parodied in DmC. The punk movement was all about saying and doing whatever you felt, regardless of being "nice," if you wanted to swear, you swore, because it was usually an emphasis on contention or overall anger, and an off-handed refusal to bow to political correctness. Dante's use of vulgarity is based on that exact element - he absolutely hates demons for how they've ruined his life, and he finds no redeeming qualities. Dante literally has a contentious relationship with the demons (sans father), and that anger shows itself in raw violence, which he revels in, and how he speaks to them. He speaks less vulgar to other people, and actually cleans up his mouth a little bit around others, like Kat, out of respect it would seem. I actually knew a few people who could be considered actual "punks," and their behavior was easy to discern. It's just about saying and doing what you feel, regardless of how someone might be offended.
The antagonists' use of vulgarity accentuates different aspects of their character as well. Poison is vulgarity personified, and speaks as such. Barbas is a lot of bluster and hot air, and what little vulgarity he spews is from a standpoint of trying to sound superior (much like O'Reilly, whom he parodies, belittling people he disagrees with). Lilith's bit of vulgarity comes from a similar place of condescension, as does Mundus', where they literally think that everyone is beneath them, and it's incredibly foolish to challenge them and their 9000 year reign.
Dante responds to their behavior in kind, in his own way. It's that whole idea that while classic Dante responds to things with dry wit and horrible jokes, DmC Dante does so while seeped in anger. Dante's tiny "F#ck you" exchange with Poison is often blown out of proportion, and was both started and ended by Poison. Dante's one response there was really just a "Well, f#ck you too!"
But, this is all it is. It's something that's used in the real world quite a bit, usually out of exasperation or anger. To think it was all done just to sound edgy is really dumb. It's imposing an idea onto something that isn't there, just to be mad at it. I can only imagine that people who complain about it a) lived or still live very sheltered lives, or b) are just complaining to complain.