I think the bigger issue here is that you are obviously uncomfortable with the idea of approaching people in public and your parents are treating this as irrelevant and something you are supposed to just force yourself to do it anyway despite feeling like the situation is wrong and threatening.
Unfortunately, this is normal behavior for them. They exhibit virtually no empathy and constantly talk trash about what expectations I don't meet. They would rather laugh at me and insult me for having issues than actually help me. I'm on my own. They will spew the most vile filth imaginable, and when I insult them back, they suddenly get all pearl-clutchy and tell me that the Bible says I have to respect them no matter how awful they treat me. I tell them "Respect is a two-way street. You don't have to be nice to people who make your life hell" and they go "B-but the BIBLE!!" They are cry-bullies. And their parenting was so psychotic that it radicalized me into becoming progressive. My brother, devout follower of their teachings, grew up to become a literal cat killer. And they treat him as a perfect child and ask why I can't be like him. Yeah, uh, no thanks.
As a defense mechanism, I eventually learned to be contrarian. Whatever my parents said, I would take away the opposite lesson. Where they were rude, I was kind. Where they were discriminatory, I was inclusive. Where they promoted certain kinds of people as superior, I believed that no kind was inherently better than any other. Instead of ignoring suffering, I believed in helping those in need. The person I am resulted from my survival of this environment, not an embrace of it.
But this contrarianism prevents me from taking away nuanced lessons, and that means I need to intentionally seek that nuance. By asking about this issue, I hope to gain an understanding of some of that nuance, at least enough to help me continue to grow instead of falling into defeatism.
Yeah, I specifically mentioned to my parents seeing an attractive employee stocking shelves in the grocery store, and they said that I should have approached her. She was clearly busy when I passed by her. I just kept my distance and casually thought, "Wow, there are plenty of fish in the sea. I'll definitely find one eventually, in a more appropriate social setting."
Not once did it cross my mind to strike up a conversation with a busy employee, but they insisted that I should have. In my mind, the fact that it's easy to find women that I find attractive is proof that I don't need to go out of my way for one. Attraction is not a quick time event; to me, it's a reminder of abundance, of just how many chances I have to find someone. I don't need to do silly stunts or disrupt busy people. I just need to keep creating social opportunities for it to happen organically, and eventually it will. I think my parents saying that I have to chat up every woman that I find attractive no matter where is silly and neurotic. I believe being patient and not stressing over every "missed opportunity" is the best way to go.
Besides, this thread is proof that I'm not ready for a girlfriend in the first place. It would be great for me to practice talking to strangers casually and making some friends first. That way, I can get comfortable talking to people in general and build my confidence.