Is it possible to change the style of the dropdown for filters?

The dropdown style is based on the browser's style definition and can't be modified easily

The different browser types do not really allow us to style a form input element, like the dropdown, properly.
It can only be masked with a completely custom solution, which is prone to introduce glitches and problems across browsers.
That is why we decided to go with the browser defaults that show when opening the dropdown when we first launched the theme.
We have added this to our list of enhancements for a future update.