To remove shadows, I commented out all lines relating to shadows.
Style 'xfcedesktop-icon-view' (~ line 927). In ~/.themes/MyGreybird/gtk-2.0/gtkrc, the code determining the appearance of text on the desktop is in the section titled
To distinguish the copied local version from the system one, I renamed the local version MyGreybird. I first copied the entire Greybird folder from /usr/share/themes over to ~/.themes which I created in my home folder. To remove the shadows, one has to edit Greybird's gtkrc file. In what follows, I'm using a plain background similar to the ones in the question with Greybird as the theme on Xubuntu 18.04.1. So, with a light background, the shadow ensures some legibility at least if the actual text is also light. If the text is light, the shadow is dark.
At the outset, I should point out that one reason for including shadows for text on the desktop is to ensure that the text is visible even if the user switches to a differently colored background or changes wallpapers.