The 3D Viewer application on the HoloLens is a good choice for loading up 3d objects, and it does seem to support .obj just fine! However, it is just a viewer, and the controls only have Y axis rotation enabled on the widget.
"Up" is a fuzzy concept in 3D spaces, and the .obj format doesn't have any relevant data about that in this case. The preferred format would be .gltf or .glb, but if you're working with .obj files, you're going to have to correct them every now and again. You can correct the orientation of the .obj's mesh in a 3D modeling tool, such as Blender or Maya by rotating the mesh, and re-exporting.