Hi OP, I work in environmental policy as a legislative advocate for a NGO, and I can tell you that you do NOT have to major in public policy to work in this field. I majored in French, then went to law school, then switched careers. My colleagues majored in everything under the sun. This is a field in which you rise to the top because of your passion, your intelligence, and your people skills, not because of what courses you took in college.
Another story: my husband went to MIT in electrical engineering. He hated every minute of it and barely graduated (he had to repeat one course requirement that he failed the first time and got a D in the second time), but his engineering degree actually turned out to be extremely useful in the non-engineering career field he pursued. You don’t always have to make a career in the thing that you majored in.
If your parents won’t pay for any degree other than an engineering degree, then get a degree in engineering. That doesn’t mean you have to become an engineer. And if you’re truly passionate about environmental policy and civic engagement, you will have a career in that field.