Would a professor be angry if I neglect to take classes within the research I'm working in as an undergraduate? I am an undergrad currently working in the lab with a great professor and doing interesting work. I promised the professor that I would take more relevant courses related to the research I'm working on to help me with my research. 

However, I found that there are some other courses that are more interesting to me and more marketable as a career skill. I want to take those instead but also continue working with him, but do you think he'd be angry if I went against his strong recommendation to take more relevant classes?
The professor can certainly be angry with your decision to go against his recommendation; however, this is far more likely to happen if you do it without explaining him several things:


your intention of not taking the courses he recommends
your motivation to take the other courses instead
and most importantly, your motivation and expectations from working in his lab


You certainly don't have to follow his advice and try to explore as many options as you want as an undergraduate, but I would give your professor an explanation BEFORE and a chance to make his points one more time. If the professor is actually "great" and professional, he would totally listen to you and understand your decision – nothing to be mad about.

Sometimes, professors treat some of their undergrad assistants similar to the grad ones. That is usually a good sign – you seem professional and valuable enough. However, this comes at a cost of them unintentionally assuming you want to continue working in their lab forever. With you clearly explaining your reasons, motivations, and aspirations, you have a chance to be as professional as you can be and maintaining the best possible relationships.