How much does the major you graduate from college have to correlate with the career you plan to pursue?

If you know you're not going to be a chemical engineer, then don't major in it! Even though your major definitely doesn't dictate what you end up doing, it's good to be studying what you might want to do.... especially if you're spending money on those classes. If you're not sure, start exploring. Don't lock yourself into something you're unsure of... or sure of not wanting.

I agree with the other answers that they don't necessarily have to match exactly, but should at least be somewhat related, especially as jobs today become more specialized. Some 4-year colleges offer nonprofit management as a minor or focus area if that is something you'd be interested in. Strong writing and communication skills are very important in the nonprofit sector, so you may want to look into studying those areas in addition to the others mentioned above.

They don't necessarily need to match up, but you will need some kind of experience that relates to the job you want when you're hitting the job market. Volunteering, freelance, internships, etc. at nonprofits. One option is to tutor at your local school. That will give you experience working with families.

I agree with Julie that your college major and career don't necessarily need to match up. I would add though that there are other college majors (public policy, social work, even civil or environmental engineering, etc.) that would be a much closer fit to the types of jobs available in the nonprofit sector. My question to you would be why you want to major in chemical engineering if you have don't have interest in working in this field?