Do you have to be a 'math person' or a 'science person' to be successful in STEM?

TL;DR: No, you don't need to worry about this at all and should forge ahead with your interest despite this concern you have. You don't need to be a math or science person (at least not in the way you're defining it in your question), for two reasons:

1. "STEM" may sound like a small set of topics in school, but it refers to an unfathomably huge set of industries and occupations, many of which you can definitely thrive in without being what you currently consider a "math person" or "science person"
2. Even if you're not a "science person" or "math person" now, you can certainly become the math or science person you need to be in order to thrive in the occupation of your choice (with rare exception).

More details below.

Point #1: STEM is huge

I think it will help to point out that what educators call "STEM" corresponds to a set of industries and occupations that is absolutely huge: pharmaceutical research, computer programming, building bridges, managing fleets of giant ships, architecting buildings, studying the cosmos, nursing, managing technology product development cycles, pharmacology, database management, designing motorcycles, and about a million other jobs (literally). You can't thrive in these jobs without learning about a variety of science and math topics, but that doesn't mean that you need to immediately have an intuition for those topics from day 1. And not all math or science topics will be necessary for your occupation. For example, as a programmer I end up using a lot of logic, a lot of reading comprehension, a lot of problem solving, and a lot of interpersonal communication skills. But algebra plays only a minimal role and calculus is never used in the kind of work I do. But another programmer in a different context might use a completely different set of skills. If you can be a little more specific about which specific sub-sections of STEM interest you, we'd be happy to share more specific information about what skills you do (and don't) need.

Point #2: You can become a "math and science person"

What Lily H. said in the comments on your question is dead-on. I think you're actually facing a much more serious risk about something critically important: you must not fall victim to a fixed (entity) mindset. Basically, you're in one of three states right now: you're either...

1. One of a very very small number of people who suffer from a disability such as discalculia, or
2. One of a very very small number of people who have a savant-level math and science intuition that nobody else will ever match like Einstein, or
3. You're basically like 99% of the rest of the population who has to, and can, learn math and science concepts the hard way.

Based on what you wrote in your question, you're clearly in the third group. So I'd say normally that you should just continue to have faith and be persistent and seek out teachers who are willing to experiment and find the right methods to help you learn efficiently.

But in your case, I want to encourage you to watch out for something potentially dangerous. Over the past 50 years, researchers (such as Dr. Carol Dweck, one of the titans of psychology) have demonstrated definitively that there is a much bigger factor that affects your academic success in subjects like math than genetics, than early childhood education, and even than instruction: whether you have a "fixed mindset" or a "growth mindset". Dr. Dweck and others have shown that if a young person believes that intelligence is "fixed" or "innate" or that some subjects just aren't accessible to them (e.g., "I'm not a math person"), then they dramatically underperform peers who believe that intelligence is "developed" or can be "improved with practice" or that any subject can be learned. And this effect is massive. Not only that, it's completely reversible! Psychologists have found that students who start in a fixed mindset can adopt a growth mindset within just hours, and see results nearly immediately. It's exceptionally powerful, and I bring it up because I want to encourage you to remember that you must have a growth mindset at all times if you plan to build the skills you need to thrive. I sense in your question someone who is fundamentally confident and optimistic and a great communicator. If you can bring that together with a growth mindset, you will truly thrive. What Lily H. said is right: use your creativity to think outside the box. And don't forget that the only thing that can make you "bad at math or science" is believing that you're bad at math or science. I believe in you! Source for my perspective: I run a technology nonprofit (CareerVillage.org), am a programmer, and hire programmers and others who would qualify as STEM professionals.

Source for the data on growth mindsets: The Wikipedia article on Professor Dweck and Professor Dweck's website and the research article that covers how growth mindsets work.

STEM is Science, Technology, Engineering and Math. So, even if you have not graduated in any of the STEM fields. you must at least know the fundamentals in them.

For Math, you need to know Algebra 2, and Geometry at the minimum.

For Science, know the basics of Physics, Chemistry and Biology. Example: Bio-Chemistry = Bio+Chem but also involves elements of Physics. Physicist= Physics + elements of Chemistry.

For Technology and Engineering, it would be great if you knew about Java( a computer language). Tech and Engineering are fields where you need multi level knowledge like how to build gears/buildings/robots/machines/websites and now a days Computer Science is ubiquitous and in tech and engineering fields, learning how to code seems to be one of the things that is highly recommended.

GOOD NEWS: There are so many sites where you can learn Java or Python for free like codeacademy, pluralsight etc. Check out your local libraries if they offer free computer language courses either at the center or online.

Hope this helps!