I was able to fix most issues with apps using hardcoded colors by changing two colors in
/usr/share/themes/lcars-bridge/gtk-2.0/gtkrc

First the text colour

color["DefaultTextColor"] = "#CC9900"

this is a bit darker shade of yellow than in the original theme. This way it's readable on both dark and on bright background. -> fixing the yellow on white issues in apps like Skype and Video Center

color["DefaultBackgrdColor"] = "#FFFFFF"

Reverting default background color back to white. -> fixing the black on black issues in apps like OMWeather.

Doesn't have a big impact on the overall appearance of the theme. The only annoying side effect is, that the border around some buttons is still black.

Or another combination that doesn't break the appreance of the theme too much is
color["DefaultTextColor"] = "#CC0000"
color["DefaultBackgrdColor"] = "#F1DF6F"