Hi,
Thank you very much for the details!
Well, it highly depends on the browser and device. Some devices allow more customization, so less, some does not allow anything. Apple devices are especially very problematic, they rarely respect any customization whatsoever.
Usually Windows/Linux Chrome is the most customizable one, and Safari is the least allowing (in my experience).
Are these post type, taxonomy or custom field filters? I’m asking because there is a different drop-down layout, which may work better cross devices and has more room for styling.