This may be a bug in OBS-Studio's display capture not properly inverting colors of cursor.
Workaround:
1. In OBS-Studio display capture settings, turn off "Capture cursor". If not off, it will incorrectly draw black on cursor that suppose to be inverted.
2. Use Windows magnifier. Press windows-key + "+" button, then zoom out all the way (windows-key + "-"). Magnifier draws a properly working cursor on the screen that will be captured by OBS-Studio's display capture with "Capture cursor" off.
If on windows 7, windows Aero need to be enabled
Edit: windows 7 magnifier might not be compatible with extended multi-monitors.
Another bug: When using windows magnifier, and is zoomed in, with "Capture cursor" enabled, there is a double-cursor problem. Again, turn off "Capture cursor" to workaround this.