Yes, the sheer stripe, brow stripe, and bottom are originally gelcoat, colored that way as the boat was built. But you can certainly change it. Gelcoated boats are painted all the time for one reason or another. Gelcoat is a great material, but so is two-part LPU, and that's often used as original color on boats these days -- it's that good. Shine and gloss can last 20+ years with care (and care mostly means keeping out of harsh sun as much as possible; but it'd still look much better than the equivalent gelcoat given the same light level of care (vs. laborious compounding and polishing like you might be giving gelcoat after the same time/conditions elapsed). Basically, the two-part LPU just looks good without too much care, and will last a long time -- even longer if you don't keep it in high UV areas all the time uncovered.
A caveat is that two-part paint is not good at or below the waterline - gelcoat is still better there (or bottom paint). Also once damaged, the two-part paint is a little tricker to repair, whereas gelcoat can be filled in, and one-part paint can be added to.
You can do it yourself, or have it done. Two part paints are serious business when being sprayed, so you need not only a respirator, but a supplied air type. Rolling/tipping/brushing is not quite as bad, but still something to take good precautions with.
One part paints work too, but the shine won't last nearly as long and they are not as hard/durable (but they are easily touch-uppable). If I wanted a good-as-new look, I'd have the color areas sprayed professionally with two-part, myself. To me, one part paint looks better on something like a wooden boat, where you don't expect it to look like "glass." But that's just me. I have seen some amazing one-part paint jobs, but even so they won't last as long or be as hard/durable as gelcoat or two-part paint.
I did see where someone with a black-trimmed 22 had it professionally sprayed and changed to maroon (but bottom paint on that section below the waterline). If I didn't like the trim color on mine, and/or when it wears out beyond the point of compounding/polishing, I wouldn't hesitate to have it re-done in two-part LPU type paint (Awlgrip, Sterling, etc.) It will cost some money, but then the material and labor are both expensive (some places might let you prep it yourself).
The red is a great color, but is prone to fading with a lot of UV.
It could be "fun" to have a unique color that no other C-Dory has :thup