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I avoid approaching women in public because I believe it's inappropriate. My parents say that it's a necessary skill. Who is right?
The unsatisfying answer: you're both a little bit right.
You're correct that times have changed somewhat. But I think it's overkill to say that "approaching women at all unless you have business with them is disrespectful and borderline harassment".
Of course, context matters a lot. Don't bother women at their jobs, the bank is not a lady zoo. But in a social situation where you would expect to meet other people, it's fine to strike up a conversation with strangers or even ask them out.
However, by your own admission you don't get out much. So I'm assuming you don't get a lot of situations like bars or parties where this would happen. So I would try networking in your community, develop some hobbies, go to functions where you might meet someone in this manner.