If there were no genders, we'd only need one kind of bathroom. If there were no genders, we'd never again see a commercial that says "strong enough for a man .. but PH-balanced for a woman." If there were no genders, we'd never have men's magazines. We'd never have women's magazines, for that matter. Ringmasters at the circus wouldn't say "Laaaaaadies and Gennnnntlemen." I think the biggest change would be the bathrooms, though. I understand some colleges actually already have uni-gender bathrooms, and apparently most people are totally used to them by now.
If there were no genders, the list "50 reasons why a beer is better than a woman" wouldn't be floating around the internet. There wouldn't be any need for the newsgroup soc.women, either. Guys (except there wouldn't be any guys) wouldn't sit around bars and say things like "Women! Who can understand them?" and then all the other men in the bar nod sympathetically. The cartoon Cathy would no longer be funny. For that matter, Beetle Bailey wouldn't be able to run the jokes about the general ogling his cute secretary, so they'd be reduced to showing the sergeant beating up Beetle Bailey every single week.
If there were no genders, we wouldn't have a women's studies major. The book Men are from Mars; Women are from Venus wouldn't be on the best-seller list. Neither would Iron John, or Women Who Run with the Wolves. No one would ever say "Oh, that's so like a man," or "Oh, that's so like a woman."
If there were no genders, there would still be wars. People would still kill each other. People would still be racist, or hate other people because of who their parents were. There would, however, be no sexists. Missiles would still be built. We would continue to spend billions of dollars on defense against imaginary enemies. Politics would still be dirty. As would lawyers. People would not be perfect.
It's possible that there would be less anorexics. It seems quite reasonable that abortion would be less restricted than it is now. Maternity leave would be mandatory and considered a normal part of life and work, except it wouldn't be called maternity leave. We might, as a people, be less violent. Then again, we might be more violent. Sex might be less restricted, less something to be ashamed of and more something that everyone does; and something that everyone admits they do. Then again, perhaps not.
No one would self-identify as a heterosexual, or as a homosexual. Still, there would probably still be people that looked for certain physical characteristics in a lover. Marriage, of course, would be acceptable between any two people who truly wished it.
If there was only one gender, children would grow up not knowing any other way. They would probably be shocked and horrified at what they would perceive as arbitrary segregation in other cultures; exactly the same reaction we would have if we found out there was a people that separated those with green eyes from those with brown eyes. This class probably wouldn't exist, or if it did, it would be in the school of philosophy. Or perhaps the school of medicine.
It might be that the people would have no physical difference from us. It might be that there would still be some people who had a penis, and some who had a vagina. The difference would just be that no one would care. They would have more important things to worry about, like how to exterminate that vile race of non-carbon-based life forms recently discovered in the next galaxy over.