What clients do
Apple Mail and Outlook keep explicit colours. Gmail on iOS partially inverts light backgrounds. Outlook on Windows can invert everything in a message with no explicit background.
Set every colour
Give the card an explicit background colour and explicit text colours. Clients that respect colours then show the card as designed.
Logos
A dark logo on a transparent background disappears on a dark card. Outromail puts logos on a small white plate when the card is dark.
Test
Outromail's editor has a dark-mode toggle that simulates the three main behaviours.