Your question indicates much confusion about the subject and some inaccurate information. Rayleigh scattering does not mean that blue scatters more in any medium. Also, blue can Reyleigh scatter in a particular medium (e.g. Earth atmosphere) and Mie scatter in another medium. The scattering intensity graph decays with $\lambda^{-4}$ but the maximum scattered intensity wavelength depends on the particle cross-section relative to the wavelength and the observed dominant color also from the distance of the observer in the case of unpolarized white light. As a rule of thumb, RS occurs when particles in the medium are less than 1/10 of the incident wavelengths. So according to the above there are mediums that can for example scatter more orange color when white light is incident or other mediums that scatter more green light and so on.
For particle sizes larger than λ, Mie scattering predominates [6, 12] and for particles that are much larger than λ, a third type of atmospheric scattering, known as nonselective scattering, occurs [13]. A description of this last type of scattering, which can be considered as comprising a combination of Mie scattering, absorption, and multiple scattering, is outside the scope of this entry. Nonselective scattering is not wavelength dependent and is the primary cause of haze in the lower atmosphere. Water droplets and large dust particles can cause this type of scattering.
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source: https://link.springer.com/referenceworkentry/10.1007/978-1-4419-8071-7_218
Imagine non-selective scattering medium category of a medium as a combination of all the above, Mie scattering, absorption, multiple scattering etc. that scatters all colors equally or partially absorbs or mixes colors due variable scattering and thus wavelength independent.
Mie scattering opposite to some may believe is also wavelength dependent but its scattering intensity graph flattens out the more the particle size is larger than the incident wavelength (see fig.6 in above link). So it becomes for large relative particles color independent. Milk is characteristic example of pure Mie scattering.
This is mainly due to the fact that diffraction contribution starts for relative large particle to become important, the EM waves just slide and curve over the surface of the particle in the forward incident direction and are less scattered thus the scattering pattern is more like an antenna lope:
The diffraction contribution is most readily discerned at a distance from the sphere and is strongly peaked in the forward direction. Thus Mie scattering produces a scattering pattern like an antenna lobe with a forward lobe that becomes more intense and sharper with increasing particle size.
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source: https://link.springer.com/referenceworkentry/10.1007/978-1-4419-8071-7_218
All wavelengths are scattered more or less in the same direction relative to an observer therefore there is no or very little variation in the scattering angles among different wavelengths thus the observer gets the same amount of color components of incident white light therefore the observer will see ideally white in Mie scattering for white incident light.
image credits: https://tinyurl.com/3xwwaknn
