Maybe something with the OLED or RFID library is faulty and forces this effects...
As I wrote above - each of them in single use is working - both together not :/
I hope to find the error - because I need both.
But thank you very much for your information - that on your ESP8266 both is working at the same time.
This is a good hint, that I should look at the libraries and fix it. Hardware issue would be terrible in this case.