I think the site linked to and the people in this thread are not a part of the problem, they are just a medium through which the problem is pointed out. A lot of people get easily offended by it, but I'm far from the only person who thinks great strides can be made away from sexism, racism, homophobia, etc. by highlighting the problem and laughing at it. Really that was the premise of that old sitcom "All In The Family" in which the protagonist of the show was a bigoted old man. Many people hated Archie Bunker, but most people got that the show was laughing at bigoted old men rather than with them.
I think there are two things at issue:
First, bigotry in any of its forms should not simply be forgotten. Racism in the United States was so bad in the past that people of African descent were considered livestock. That's horrible, but our response to that should not be to shove it away in a corner and pretend it didn't happen (like the recent controversy over editing the word "nigger" out of Huckleberry Finn) but to admit openly that it happened, and that it was wrong. I believe pretending that because slavery was legally abolished over a century ago, it doesn't matter to us today just allows us to turn a blind eye to the racism that lingers on long after the fact, as well as the different forms of slavery that still exist in this country today.
Secondly, context is important. Just yesterday, my daughters were watching an old episode of "The Jetsons". I was only partially paying attention to the TV, but I soon realized that the episode they were watching was essentially a half-hour of "Wow, women sure are awful drivers" jokes. Now such jokes are occasionally made in more recent sitcoms, but usually it's intended to mock this stupid stereotype; it's clear the writers and producers of "The Jetsons", while using it for humor, were perfectly serious about the matter, as indeed, every female driver in the episode (with a single exception used for other comedy purposes) was a complete menace to society. Thinking about it later in the day, I realized that I really failed as a parent by not talking to my daughters about the episode, and the outmoded thinking it was presenting. I do know that my daughters have been told by me in all honesty that "Mom is a much better driver than I am," and I hope that helps, but I worry about it.
tl;dr version: Yes, sexism is a problem, but you should probably lighten up.