I have a logitech unified receiver connected to one of the front usb port of the nuc. It works, but when i insert an usb key to the second port mouse/keyboard are not working anymore.
I've had the same issue with my NUC8i5BEK and with a previous NUC7i5BNH. It seems that there is some RF leakage from the USB wiring or from the board which interferes with the Logitech dongle's radio for controlling the mouse/keyboard. One solution is to get a short USB 3.0 extension cable, male to female, and plug the dongle into the extension. I have a 1-foot extender which puts the dongle far enough away from the NUC that there's no interference.
Amazon has dozens of them in various lengths:
Apparently Intel needs to do a better job of shielding the wiring/USB ports.
Edit: But then again, it may be the interference is coming from whatever you've plugged into the USB port next to the dongle. Cheap flash drives are notorious for RF interference, especially when you're accessing them by reading/writing files.