I am using Word 2016 on Windows 10. I cannot get rid of the white background for text when I apply shading to specific table cells, as you can see below:
The shading is applied to the cell, but choosing any other value (text, paragraph, table) also results in the same behavior.
I am a seasoned Word user and this never used to happen before.
OK, I think I've got this sorted. The text in my cells uses the Normal style and had exactly the problem shown in the question - a white highlight against the cell shading colour. I fiddled with modifying the Style's Borders & Shading - but the Fill was No colour and the pattern was Clear, so all looked OK.
Disadvantage: Any Bold, Italic, etc applied to existing text will be cleared and will need to be re-applied.