Will medical institutions reject an applicant based on being 28 years of age?

In the US, being 28, 30, or even 40 is not a problem for getting into med school. I was 26 when I was admitted, and I was far from the oldest in my class. In fact, by my senior year, they had admitted a couple of students older than my current age at the time! If you haven't been slacking off in between college and now, it could make you even more competitive because you can point to past successes and have interesting stories for the interviewing process. A typical medical school in the US could easily fill each class with biology and chemistry students fresh out of college with high GPA's and MCAT scores. Someone older might have all of those, plus the strengths of a rigorous career or valuable experience outside of medicine. You can differentiate yourself from the rest of the pool.

Now, to the main issue of age. By the time you finish the pre-reqs, ace the MCATs, and finish 4 grueling years of medical school, do you think you'll have the energy or motivation to do an even more intense additional 7 years of neurosurgery? Neurosurgery is competitive enough that they can pick whatever candidate they want. While not a given, you will likely face some "soft" age discrimination for intense/competitive residencies and fellowships. For this stage, you'll have to work extra hard to convince them you can physically compete with the youngin's, much less complete/survive the program. Once you finish your neurosurg training, you won't have problems finding a job. Once you're board eligible/certified, no hospital cares what school you went to, how old you are (to a point), or what you did in the past. All that matters is what you can do for them, ie increase billing by a zillion dollars.

You can get more detailed responses and support from the forums.studentdoctor.net website. There's even a sub-forum for the "non-traditional" applicant, which honestly, isn't so non-traditional anymore!

Being a few years older is definitely not a problem for entering medical school.

I know people who have gone off and done other professions before figuring out that they actually wanted to be a doctor. The difference between being 20 and being 30 just isn't that much, and you even may have an advantage in some ways from having more maturity and a better understanding of why you want to be in the profession.