It depends on how well you can adapt and how many people are willing to support you. From a "color-seeing perspective", the colors that we see can be described as "arbitrary" and "following patterns". Arbitrary in the sense that people have come to prefer certain color over others - in the case of text, our "advisors" are always insisting on gray text color. If it is dark black, they get annoyed. (As a programmer, you could consider me color-blind in the sense that I don't really care a whole lot, I just change the color when it is asked for). "Following a pattern" in the sense that they are choosing gray in order to prevent the text from appearing too prominent in the page.
So as a programmer, I just change the color and to me it is arbitrary. If I wanted to improve UX, I would follow the above rule with graduations. That is a colorblind example, but colors are the same. They follow certain rules, certain colors go with certain colors and not with certain colors, and people like certain colors and not certain colors. There are 255^3 colors that are possible on the web, but I would speculate that most of the colors used are in a very small range. Which means that there are a number of "acceptable" blues, "acceptable" yellows and "acceptable" reds which you can learn and which may even be specified for you. You could learn maybe 3 of each and learn rules of color from others, either online or by your own research. Do you know that "red" is a very "dangerous" color and has no place except for alerts, warning, negativity, etc.
That is a complex science, but you might be surprised to think that color see-ing is predictable. If you are good enough at UX, then you will just have someone else around you who fixes the colors, and some companies will support you in this. But ideally, you can just learn when to use dark blue, when to use light blue, the different shades of blue, etc and the colors that nobody wants to see like turquoise, etc. I'm not going to write that for you, but with difficulty, you could find that and begin producing designs, pretending like you know the colors. Take a look at this page? How many colors? I count: 2 yellows (answer box and tooltip), 2 blues, 1 blue so dark it looks like black (the "X" in UX), 1 dark yellow (brownish - ask question button), 2 greens and 1 red. Difficult, yes, but not rocket science.
Additionally, the answer by "Miles McCrocklin" has a rule for you. Check it out and learn it.