It's how they bathe the dust and pollen off their wings.

I thought butterflies shouldn't get wet?

They can get wet, because their wings are waterproof. They would sort of have to be. If you touch their wings, you can remove the protective waterproofing, which is why you have to only pick them up a certain way, with their wings closed..

When the first emerge, their wings are wet and they have to dry before they become waterproof. If their wings are damaged before they are dry, they won't be waterproof in the damaged areas, which is why you should leave a newly hatched butterfly on the ground alone.

https://www.sciencenews.org/article/how-butterflies-stay-dry

Glad to have this good answer! And yet, there are other explanations on the web - and they don't agree with each other!

There is no waterproof substance on butterfly wings that can be removed by handling. There are scales, and those are easily removed when handling. Removing too many scales would alter the butterfly's natural appearance and this could have negative effects. The photo in the above link is not a butterfly wing -- scales overlap on real wings. The researchers did not use actual wings in their water drop experiments. Beware of pseudo-science websites.

Monarchs are big butterflies and strong flyers that fare well in rain that would make most butterflies seek shelter.