If any future users scan this post, then here is an approach I used (ArcGIS pro 3.2):
1) select project ->options->Map and Scene -> Spatial Reference -> Choose Spatial Reference :
select 'NAD 1983 Zone 5N' or whichever for your particular problem.
2) start a new project, and you should notice that the basemap conforms to this new coordinate system.
3) add the layer/shape file (which now should match the basemap/project).