Thank you, Lydia. I hope it can help you.
Lydia, I think you have to consider that it is their problem, not yours. Some people are incapable of showing any compassion or even courtesy (and I mean, having the courtesy to not stare. You cannot restrict your movements because somebody might look at you.
I use a cane because it allows me to walk faster, balance better, not trip over curbs or bumps, etc. Without my cane those things happen, as well as me bumping into people who are walking towards me. I see them, and my legs just carry me right over there and bump into them. That sounds kind of silly, and it feels silly, but that's the way it is. I suppose a benefit to me is that I grew up in an environment where we all didn't care what the neighbours thought, or what other shoppers in a store thought. Friends who would abandon you, or change the way they speak to you, or consistently cancel meetings such as lunch or dinner engagements, just because they are embarrassed about your symptoms, are not really friends. No matter how much you may like them. The problem is their shortcoming, not yours.
Read and learn as much as you can about Parkinson's disease and be prepared to answer questions because those people who are indeed your friends will be interested and will want to know the details and how they can help.
One thing you might like to try is to smile and say 'hi' to others you come across on the street or in a social setting. Be prepared in your mind that they may just walk away, but you will meet some good people who are confident enough in themselves to engage in a conversation - the beginning of a new friendship.