Gas giants like Jupiter and Saturn have bands of different colors in their atmosphere. These are due to the rotation of the planets. Stars rotate too, so why do most stars have patches/blotches of color rather than having latitudinal stripes?
Just rotation is the wrong tree to bark up on.
You see color variations on gas giants due to differences in composition, i.e. ammonia vs. sulfuric acid clouds on Jupiter, which are transported differently on the rotating planet in the up/downwelling bands.
Spots on stars originate due to very different physics. At the temperatures which are prevalent on stellar surfaces, molecules are mostly dissociated and ionized, we call this state a plasma, so no more colour effects due to ammonia or others. Star spots are concentrations of the local magnetic field, which is coupled to the plasma dynamics. The magnetic field pushes the gas aside and lets the surface cool locally. This makes dark spots that you see on stars like our sun.
There is a transition region in terms of surface temperature of 2000-3000K, at the masses of brown dwarves. Those failed stars seem to exhibit dark bands on their surfaces, which are thought to be due to absorption from exotic, high-temperature molecules like TiO and VO (Titanium and Vanadium oxide).
The atoms in stars have disassociated electrons at random distances, they are ionised, and the energy converted to light is at a continuous spectrum of wavelegnths and colors.
The heaviest elements with a potential for color fall into the star.
Color bands from stars come from colder atoms in the high corona, which can cool and have fixed electron orbits which output fixed wavelengths.
To have colored stars you would need an elemental veil cloud that acts as a color screen.
Gas giants don't emit radiation, they reflect it. Due to their mixed composition, there is different amounts of light absorbed in different ways, giving them their distinct colours.
Stars on the other hand glow because of the energy that is produced at their core, and their composition is almost purely hydrogen.
So because of their high temperature, and almost completely or composition, stars glow in just one colour, while gas giants have distinct colour combinations.
While stars don't exactly glow in just one colour, they emit radiation in a predictable manner (according to Wein's displacement formula) which gives the relationship between the temperature and the wavelength of the most emitted radiation