When I turn on “High Contrast” from GNOME’s Accessibility menu, the background color of cells in LibreOffice Calc are no longer visible. They always appear white. Only when I disable High Contrast do the true colors show up. How do I resolve this issue?
You have to realise what high contrast does, it turns off display of background colours to improve contrast.
See Accessibility/Accessibility-dev - The Document Foundation Wiki
If you have high contrast set in the operating system but don’t want it in LibreOffice then you can turn it off for LibreOffice.
Click Tools - Options - LibreOffice - Accessibility and set High Contrast to Disabled