I now bought an LG 55EG910V OLED TV. I can see what you talked about. It's harsh on my eyes - it doesn't feel too different from any standard LED-backlit monitor. I tried many kinds of settings and am still searching for a solution, but this is going to be tough. It's in no way comparable to my OnePlus 3.
I learned LG, in their TVs, use white OLEDs only + color filters.
I also found this short article where they claim their OLED TVs emit 3x times less blue light than backlit devices: http://www.businesskorea.co.kr/english/news/ict/6908-blue-light-hazard-lcd-tvs-may-emit-3x-harmful-light-oled-tvs
As there are no further links or sources, I don't know if it's true.
Eyes are red, burning, and if I watch for too long I get small headaches.
I plugged in my PC with a supposedly still "good" setup (Windows 7 + old NVIDIA card), but this didn't help at all. It seems the eye strain is related either to the OLED light or to LG's "WebOS", which is probably creating the final video output.