| There are few absolutes, think of it as a statistical process.
For some jobs it may be critical to that particular hiring manager. For another job and another boss it may be irrelevant.
Every, job, boss, company and industry are different so there's a nearly infinite number of permutations. Think of it as stacking the deck in your favor. You're subject to the luck of the draw but your odds will be better.
A lot will depend on your goals as far as your technical interests, where you want to work (geographically), who you might like to work for or what you're willing to put up with. If your goal is to live in particular place that neighborhood will have it's own set of companies, jobs and competition for them. Similar if you want to work in a particular field or for a specific company.
You don't have to be the ideal candidate, just the best one of the bunch (from the manager's perspective). In a desirable area with few openings you'll need to have a lot going for you. If the company needs people badly and there aren't many applicants to choose from odds swing the other way.
It certainly makes sense that a company will look favorably on some curriculum choices if they are specifically applicable to their industry.
On the other hand, I've seen a number of situations (especially in software) where the company didn't seem to care about the applicants' majors. They were willing to hire people with degrees in engineering, math, physics, chemistry or whatever (as long as it was a technical discipline) to do the same work if they had good experience.
I don't have any data on how GPA effects hiring (I'm sure somebody does somewhere) but the longer you're out there working the more your professional track record counts and the less your scholastic.
Supposedly, knowledge is what it's about. Yeah, I know that's an idealistic conceptualization and the real world works differently, but in the technical world it holds up better than most others. Five, ten or twenty years from now the manager interviewing you may not give a rat's rump about your GPA or minor but they will care about how you're going to get the job done. If you have that capability, and can convince them of it, you'll get the job.
PC. | 
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