I think that in Russia the opinion of people is kind of same as in USA.
Generally it is considered to think that men are more logical, more aggressive, more athletic, more competitive than women. And women are more careful, more cooperative, more gossip, more sociable, more concerned than men. And I think that women can feel a kind of discrimination in some situations in Russia. But in my opinion you can see this situation in any country. And I don't think that it means some disrespect, it means only that women are different from men and they cant do some kind of work as good as men. I don't understand how could work woman as a police officer. It's hard, kind of dirty job for men.