(a) There is some evidence that engaging in discussions on gender and taking a view nearer the "feminist" than the "reactionary" end of the spectrum sometimes results in getting hit by mass-downvoting. I'm not sure whether other (leftish?) political opinions provoke it.

(b) I don't know how much is "so much", and hence in particular whether it's true that people care about karma "so much". But the karma system is part of how LW is built; it's meant to be somewhat motivating for writers and somewhat informative for readers. Indiscriminate downvoting (or for that matter indiscriminate upvoting, though oddly one rarely hears of people complaining that this has happened to them) of a particular user's comments is liable to distort both.