No, I don't think sexism is a problem. Rape is a problem. Child pornography is a problem. Hunger, drought, tsunamis are problems. Huge companies poisoning people, land, and wasting tons of food is a problem.
Sexism? Just a bunch of people who live practically perfect lives, and have no problems, and are bored, so they create some.
I'm slowly finding this conversation too Orwellian. Why do you care about what I think?!? I might be a phedophile, a rasist, but as long as I'm not hurting other people, I'm better that 99% of the world population. I find some people (so far only women) attractive, therefore I'd like to have sex with them, if I got a chance (I don't actively seek such chances, because sex with most women is boring, in my experience, unless (my) emotions are evolved). I don't make sexual comments at work, not because I would think they are inappropriate per se (I wouldn't make comments about someone being fat either, not because I think it's unappropriate, but because I don't want to hurt their feelings even more without good reason), but because at work, I like to focus on work.
Edit: to put things into perspective: my grandmother was born in 1930s. There were 8 children. One died very young. Her father was killed by nazi collaborators. He had a job. Her mother didn't. She had to support a family of 7, I don't know how. They made a drink out of tree bark, because coffee wasn't available.
My grandmother smiles more that most people I see commuting daily on the London subway. When people say, "we have a crisis", it makes me smile and think how deluded they are...