At the intersection of North Road and Stolley Park Road in Grand Island, Nebraska, there's a stop sign with a plate below saying "OPPOSITE TRAFFIC MAY NOT STOP".

Sounds scary, as if it is warning that oncoming traffic may run the stop sign in any direction.
It would sound better if it instead said "OPPOSITE TURNING TRAFFIC DOES NOT STOP".
On the other side, there's this plate below the stop sign, saying "RIGHT TURN NO STOP REQUIRED".

I can see the railroad crossing as the reason for the setup. My guess is that the right turn without stopping is permitted because most traffic would be turning to stay on Stolley Park road. In other words, a TOTSO.
A bit redundant imo, as even without it, vehicles continuing straight would have to yield to cars from the right.
https://www.google.com/maps/@40.9019935,-98.3955777,3a,48.9y,96.37h,82.9t/data=!3m7!1e1!3m5!1siyXdhKhNzzCLKEbwp9Swjg!2e0!5s20190801T000000!7i16384!8i8192