Going vegan is fine. I'm not surprised your parents are worried though. I'm in my fifties and my Mother-in-law still worries. She loves my food though and says minor complaints clear up when she stays with me.
Be gentle on your parents, as like many people who have answered on here, they probably think it is unhealthy, unnatural etc. Try to reassure them by learning about diet and nutrition, and cooking them some really tasty meals.
http://www.vegansociety.com/ is a good source of info.
http://www.veganfamily.co.uk/ is another good site.
It is also quite a challenge learning how to cook tasty vegan food. Vegan recipes are often hard work or so wholesome they are horrible. Your Mum may be worried about providing meals for you. It is more work for her.
Soy milk, soy cream. soy ice cream, soy yoghurt, vegan margarine, rice milk, oat milk are all very nutritious and delicious (depending on brand). They'll give you lots of calcium for healthy bones, Calcium is also in dark green leafy veg. IMO all vegan cheese is disgusting and I really miss cheese.
Cakes made without eggs and butter work well. I can even make light fluffy Victoria style sponges.
Vegetable stock cubes make life easy - but watch the salt content.
A dollop of curry paste rescues anything and everything. Herbs and garlic do the same.
Love your vegetables and eat a rainbow. ( the more colours on your plate the better, red, green, yellow, purple, more green).
The only supplement most vegans agree is required is B12. The latest research shows that heavy mushroom eaters manage fine without B12 but I'd take it to be sure.
I've had cancer twice. The first time I wasn't vegan and had always eaten a normal diet. During chemo you get regular blood tests. The first time my blood tests were unremarkable. When I found the cancer came back I did everything I could to help my body beat it and went vegan. My blood tests on the second bout of chemo were so good the nurses asked what on earth I was doing as they were better than those of a normal healthy woman.
As far as being an outcast, it depends where you live. California seems to have masses of vegan restaurants and events with vegan food. Here in remoter UK I really miss being able to go out for a meal. There are places to eat out but few and far between. More and more people seem to understand though. In the UK, the supermarkets are stocking far more vegan food. At family parties I just take a couple of vegan sausages or similar and eat the veg. Most social events I go to have some vegan food even if it is just hummus and baked potatoes.
You could always compromise a bit for the sake of your Mum and agree to eat a bit of fish once a week. Ease her into it gently.