Is there anything that could change the colors of the clouds while still maintaining the sky blue? Or any other color for the clouds, except blue. You can use our solar system as a basis for this. Earth does not have to be habitable after/with the changes.
You can have red clouds and a blue sky. We do, not infrequently.
Not all clouds are white. As mentioned above, the colour of a cloud depends on the colour of the light that illuminates it. At sunset or sunrise the colour of sunlight can be yellow to deep red due to the scattering of the blue component of sunlight as the light travels a longer path through the atmosphere.
The trick - have your light take a marathon trek on the way to the clouds. The longest frequencies (reds) are most scatter resistant and those are the ones that get to the clouds and light them. Shorter frequencies are scattered along the way and do not make it to the clouds. The shortest frequencies (blues) scatter the most and might scatter back out of the air to your eye, making the sky look blue.
Sun at the horizon is the longest path through the atmosphere. Just below the horizon works too because from the cloud perspective in the sky the sun has not yet set. There are various ways one can have a world with the sun always at the horizon and possibly never setting or rising. It can come close to that at the poles and if our world were tidally locked and not tilted it would be that way at the poles all the time.
A star that has a stronger red component should work. As has been mentioned, clouds in the evening or morning are red because only the red light is getting to them. Have red light (from a red star) get to them and they will look red.
The sky looks blue because that is the color that our air scatters. As long as the star has enough blue in it's light, the sky will look blue regardless of the color of the star.
I don't know if a red star has enough blue output to make the sky look blue but an orange star probably does. The atmosphere just needs to scatter enough blue to make the cloud look red (higher clouds will look more orange than lower ones).
Unless someone who knows enough about stars and atmospheric light scattering says that there isn't one, just posit that there is a sweet spot between our yellow Sun and a red star that produces red clouds and blue skies.
The great red spot on Jupiter looks like a good candidate. All artist's renditions show that the clear sky is blue, and that's due to the rayleigh scattering. These clouds are truly red in color, not because of sunset or light filtration.
It is not known exactly what causes the Great Red Spot's reddish color. Theories supported by laboratory experiments suppose that the color may be caused by complex organic molecules, red phosphorus, or a compound containing sulphur, but a consensus has yet to be reached.
our clouds aren't blue - they are white because light gets scattered in water vapor.
If you have any kind different vapor, then the color will change.
Equally for the sky - our air tends to scatter light in just the right way that solar light tends to produce blue diffuse light and other wavelengths tend to be blocked (i.e. some UV-parts) or just travel straight.
So there's no need for these two things to have a huge correlation in color.
[Edit:] Also you could have dust storms lifting iron (the most common red thing in the universe) into your atmosphere, making small iron-oxide-red clouds. But for that your planet needs hard storms and much iron on the surface.