Ummm... do they want you to start wearing leather in your day-to-day life? Because that would just be obscenely ridiculous.
As far as if you should wear it while modeling, that's your choice. I know nothing about that business, so I have no idea what your situation would be if you refused to wear leather. I'm sure the biggest problem would come up with shoes.
So my question is... are they paying to get you started in this? Does your success or lack of success in any way have any bearing on them? Have you borrowed money from them (or are they financially supporting you)? Because if the answers are yes, then maybe they do have some say. And if you wouldn't get jobs because of your ethics, then maybe they have a valid concern. Which would mean that in order to stick to your ethics you'd have to wait until you're no longer tied to them to begin.
I would imagine that the people just starting out would have the least amount of choice. If the first time they tell you to wear something, you choose not to wear the shoes they've handed you, then do you think they'll waste their time arguing with some upstart they don't even know is good at her job yet? I dunno... it worries me a bit. I can actually kind of see where your parents are coming from (maybe). Sorry about that. But at the same time, I would let you try to do whatever you wanted on your own and hope that I was wrong.
Maybe if you're able to address your parents' concerns in a calm way and then dispell them by doing some research or something
, they'll no longer care. Good luck with that.