I love Category Theory and I also love programming so I learn both of them in my spare time. However I find that programming takes up so much of my spare time. I reason that the less thing I can do now, the better I would do them so maybe I would try to give up on programming. But I'm still very indecisive. If I'm going on the road of Category Theory research, there would be no use for improving and keeping my programming skill?
Your profile suggests that you are still a teen ager. Therefore my advice is, for now, to explore a lot of things and don't try to specialize too much in any one thing. It is a big world with a lot of possibilities.
I'm not suggesting that you give up your study of Category Theory, but there is a lot of other mathematics that is interesting and which supports that. Likewise, if programming is fun, even if hard, it will stretch your brain in a slightly different way than mathematics. That is very valuable in itself.
There will be plenty of time for specialization - even extreme specialization if you reach the stage of doctoral level education.
My advice would be to be open to areas of math that allow for programming skill. You can still take some theoretical classes and such. But there is a lot of good stuff in optimization theory, data processing, cryptography, etc. that uses both math and programming (and even sometimes other fields like OR, business, mechE for finite element analysis, etc.)
Also, if you get a broad science/math background, you may find yourself doing something even different from the other two choices (e.g. physics or crystallography) which still involves a lot of the skills and interests you have. And you will be a better teacher and maybe even researcher if you have some general breadth.
Learning how to code and code well is an incredibly useful skill in math research in all fields. (I can code, but not code well, but I've been very lucky to have collaborators who are much better than I am. Around half of my papers involve serious computer calculations)
But perhaps more importantly, category theory is one of the closest fields in math to computer science! For some examples, category theory is used in studying databases, monads are an important notion in category theory and also in Haskell, and Homotopy Type Theory is a computer science-inspired approach to homotopy theory and higher category theory. Some category theorists actually work in CS departments. I'd say that if you want to do category theory that's of broad interest, it's almost essential to have a solid background in computer science.