How did rainwater become muddy?

Well, the last time I saw raindrops on glass, I did not notice that they were particularly muddy, so I may suggest that it is not mud but acid that your rain contains, and perhaps you confused the two.

Yet once rain hits the ground, it may collect in puddles of rainwater. When disturbed, the rainwater is muddy. In this case, the answer is that the very small particles of soil have been stirred up by the energy put into the water, and they will be temporarily suspended, making the water muddy (as the water is now cloudy, and has the colour of the soil).

If it is flowing freely down a slope, the water is muddy because as it trickles, it picks up tiny particles of soil, making it muddy.

If this does not answer your question, try rephrasing it to make it more specific.