Call me old fashioned but I believe that respecting women is one of the most important things to uphold in life.

Respecting anyone is important

Yeah You're right

Okay...great. That's a sentiment...

Now how exactly and specifically do you do that?

What difficulties do you face in doing that in a potentially diverse world where a show of respect according to how you understand it, or how you think it should be communicated, is taken as a sign of disrespect?
Do your intentions trump their perceptions?

Also, how do you handle people/women who don't respect you, themselves, and/or others?
How do you reconcile it when people are trying to respect themselves but that means they have to, in some way, disrespect others?

Yes you are right