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Yup, catadioptric lenses wipe out CA from your images, they have a few drawbacks; the design means they start off at telephoto focal lengths with fixed apertures and there is a teeny tiny “hole” in the image middle (this is not a big issue, it is usually never noticeable, but it is there). They also tend to be a little heavy and occasionally need adjusting to keep the mirror part collimated. They give you pretty good images. As I recall, Minolta made a catadioptric lens that could auto focus, this was taken over by Sony who still makes the lens for one of their bodies, but no one else makes one. There are several manual focus ones for Fujilfilm’s X-mount bodies. Achromatic lenses do remove red-blue fringing, you can often find these types in those screw on macro-diopter lenses or in old box landscape cameras. But they have a problem with green fringing as it is not corrected at all. To get all three fringings, red-blue-green, folks have shifted over to Apochromatic designs. These are found in high end telephoto camera lenses and more often in refractor telescopes — the triplet design. They currently tend to be expensive.

What jerryy said. Couple more ideas: putting color filters in front of the lens can help. There are "straw" filters that look very pale yellow, which knock out the shortest blue wavelengths without changing most subjective colors much. Maybe somebody also makes a filter that knocks out the longest reds, also without changing colors much. And, if you can play a little with composition -- I mean, if your subject lends itself to this -- you can orient the edges with the biggest brightness contrast to be radial in your image, rather than circumferential. Chromatic aberration only happens radially with respect to the optical axis (e.g. the photo center if it's not cropped. I *think* there are many optical systems that are achromatic, specifically being corrected for two widely spaced wavelengths, that will tend to have green versus purple (red + blue) fringes. Picture a graph of the effective focal length as a function of wavelength, and these systems will be a smile or a frown. For some purposes (such as astrophotography) you can get much fancier and more costly optical systems that are apochromatic, corrected for three wavelengths, whose graph will slope up-down-up or down-up-down. Going beyond that, systems based entirely on mirrors have no chromatic aberration. I guess -- don't know this for sure -- that camera lenses using both mirrors and refraction, catadioptric lenses, could have less chromatic aberration than lenses without mirrors. These are generally fixed focal length, fixed aperture lenses. There are some 3rd party ones available for Fuji X, though I don't remember seeing any that are autofocus.

Fuji shooter. X-Pro 1, X-T30, X-T4, XF10, but currently on the X-T5. Based in Los Angeles. IG: @TOPSHELFJUNIOR

The bluish fringing is chromatic aberration. It is a fact of life for photography, especially for high contrasty images taken with zoom lens, and quite often for images taken with zoom lenses set to wide open apertures, maximum or minimum zoom length in high contrasty scenes. If you have software for processing images, or for converting raw images, look for tools that reduce CA, often called color fringing. With practice you may be able to reduce it to not being noticeable. There are lots and lots of tutorials on the internet about reducing CA. If you only shoot jpeg images, try stopping the lens aperture down some, or kick the zoom back a little. CA tends to be worse at the edges rather than the frame middle for what that is worth. Avoiding high contrasty scenes does work, but that is not realistic, so try to get it to the level where you can be happy with the image and do not lose sleep over it. The CA in the image you posted is not bad at all, you almost have to start pixel peeping, with a little work you can get rid of it, Your lens seems okay, based on this shot. p.s. Welcome to the forum.