Here's the definition I am using:
respect: deference to a right, privilege, privileged position, or someone or something considered to have certain rights or privileges; proper acceptance or courtesy; acknowledgment
Dismissing an entire culture or group of opinions is what gets us into these messes in the first place. And we aren't above reproach.
You can keep bringing up the example of how awful it is to kill someone for being gay and dismiss THAT culture, but since gays are still beaten, harassed and killed in the US because of their sexual orientation................
I think this is a difficult subject. On one hand, I don't approve of many aspects of many cultures. I don't dismiss the entire culture because of it. I do think that if I go to a country, I should try to abide by their rules and customs. When they come to our country, they should do likewise.
As an example, I don't think it should be allowed to obtain a Florida Drivers License without a photo from which the driver can be identified. If it is part of ones religion that they remain covered in public, not having the privilege of driving is a consequence.
In the cases of harm to others however, I think showing "respect" is akin to showing approval.
Another example: I always speak up when somebody makes racists comments in my presence. If I didn't, they would assume I approve.
This where it gets more difficult for me. Take a country like China. We know they have a dismal record regarding human rights. What should the US do? I don't think there is an easy answer.