How vital is it to get to know my professors who are outside my area of interest?

I agree with the previous post, this is not vital to your career, but it is a helpful exercise in Networking & Creating contacts these are helpful skills for anyone. Not everyone that can help you in your career development or professional development will be in your line of work. Many people take on a variety of jobs before finally landing their ideal/dream job and it is the accumulation of the skills and lessons learned by a variety of people along the way that help shape you as a professional. I work in IT for several years now, but I used to work in a restaurant and I remember what one the cooks told me years ago, it doesn't matter what dish you make it will all suck if you don't have the right ingredients. If you apply that same philosophy towards life then you could say that success is obtained by having the right ingredients such as, good communication skills, can-do attitude, and hard work ethic.
Good Luck :)

It is not vital, although you may find it personally enriching, if it is a class or discipline you are especially interested in. Many liberal arts classes also have discussion sections that are led by a teaching assistant. You can also get to know the TAs in both your technical and non-technical classes. They can help you understand their research and experience in graduate school, which may also be of interest to you.