Should students who are not majoring in marketing be required to take marketing courses?
If I understand you correctly, you are asking whether students majoring in things other than marketing should be required to take marketing classes. I would argue that all students who are majoring in some other aspects of business should be required to take at least one marketing class. Marketing is a tremendously important part of business and many business majors should have at least a basic background in the subject.
There are some types of business majors where you might not need to have any knowledge of marketing. For example, if you are an accounting major, marketing might not be very important. It would be important for you if you intend to start your own accounting business, but not if you are simply planning to work for a firm.
However, if you are going to be in any sort of management position in a firm, it seems that you would need to have a marketing background. Marketing is one of the factors that will do the most to determine whether your firm is profitable. If you are in a management position and you know nothing about a factor that will determine whether your firm is profitable, you are not going to be able to do a very good job. Because marketing is so important to the success of any business, I would argue that most business majors should have to take at least one marketing class even if they are not going to actually major in marketing.
As a recent graduate from college, I can relate a bit to what you are asking. This was my first concern when I was trying to maneuver the college scene. Why do I have to take all of these classes that will never help me with my major or in the real world? I felt bogged down by the amount of work and money, however, now that I am out, I truly appreciate all of the classes I took that did not necessarily help my major. The job market out there is highly competitive these days, and you want to do your best to become as "marketable" or employable as possible. From my experience, the employers are going to hire the well-qualified jack of all trades, over just the well-qualified. The reason? The said person will be utilized more.
I would say, if you are in a field close to the marketing field, then yes. Take it anyway :) Who knows, you may learn more in that course than others. You never know what opportunities await you.