Westerners, particularly those from the world's largest economy, generally hold a stereotype of non-white cultures being less progressive than Western cultures on practically every front. Non-Europeans are therefore assumed to be uniformly more sexist and more homophobic than Europeans in every aspect of their lives. In reality, experiences from within the same country can be extremely diverse, and one individual's horror story about discrimination may be no more representative of a culture than another individual's positive experiences.
But when we encounter examples that don't fit our stereotypes, e.g. people of color who are not as homophobic as we expect them to be, we dismiss them as anomalies or fiction, often without any real knowledge of the culture involved, or any interest in doing further research.
East Asian cultures and Islamic cultures have been favorite targets for being held up for negative comparisons with Western cultures when it comes to narrow-mindedness and authoritarianism. While not at all denying the problems facing people living in these cultures, it should be noted that Western 'feminst' writers often play up the 'oppressed Oriental woman' stereotype to the point of making things sound worse than they really were/are. And the same Westerners are often silent about the sexism in their own communities and their own families. There is still much work to be done to protect Western women in Western societies.
Many of us are the blind to how outsiders view gender stereotyping and exploitation in Western society. An Indian expatriate in the US, taken aback by the pink-blue color coding forced upon children by American retail chains since childhood, as well as the ubiquitous Barbies and Disney princesses, considered American social expectations of gender expression as harmful and limiting for her daughter. Hearing the perspectives of foreigners can be quite eye-opening and may challenge the assumptions that keep us in blind self-adulation and complacency.
We crow a lot about our progressiveness and open-mindedness, but if we are truly secure in the strength and morals of our cultures, we would not even feel the need to brag about ourselves and put others down.