This is definitely not an easy question, and the answer will differ from family to family. In the best-case scenario, you sit down with your folks and explain your ideas and interests. It has to work both ways. Once you've heard each other, you may be able to manage a compromise, like a double major. But this doesn't always work.
Some parents come from families or cultures in which older members make decisions for younger ones.
In these cases, experience is held to be the prime basis of wisdom and compromise may not be a workable solution. If you can't reach an understanding, you have to decide what your priorities are. If you're determined to follow your own ideas, you have to make yourself very clear and be willing to take the consequences. I said in an earlier column that I changed majors four times. What I didn't say was that I worked full-time to put myself through school.