Please add a tick box option within the widget setup to allow the admin to choose Near Me results even if the layers aren't turned on within the current map. Eg. Always show results "Tick Box".
Support Case:- #02916474
The reason this is happening now is because ArcGIS Online started supporting Layer List widget’s layer visibility in Near Me. This means if any layer’s visibility is off, the visibility needs to be turned on to view the result in Near Me (Near Me will not automatically turn those layers on, which used to be the case before).