Is there a way to hide dropdown arrows and radio button outlines when using a Filemaker Theme (River). I was able to use conditional formatting to hide everything else.

I have the same issue with wanting to remove the arrow from popup when I use them simply to display (on Cool Gray).  You will need to remove their theme then manually apply styles you wish.  Select an object then in Inspector > Appearance tab, Style Custom ... look for the icon with red slash through it.

 

Those four icons deal with theme.