That can be an issue. I think dark themes are primarily intended for environments with lower ambient light and fewer sources of glare, though matte displays make them more usable in other conditions.
What this means is there should be an easily accessible, systemwide toggle e.g. Android's quicksettings that asks apps and websites for the theme the user wants at that moment. This is something I've wanted for years, and I'm surprised I haven't seen more people calling for it.
God I hope that the rising popularity of dark mode will in turn raise desires for resurrecting matte displays. I miss them so much. I"m not well read on the subject though -- I hope there are no technical limitations to making high quality matte displays that would limit them (technically).
Reflections on the screen is a problem with the screen. Even when 95% of the screen is white background, things like lamps still reflect badly on a glossy screen and produce eyestrain.