This AssetPostprocessor switches the Y and Z axes of imported FBX files (and everything converted to FBX from Unity).

FBXAxesFixer.cs

using UnityEngine;
using UnityEditor;

public class FBXAxesFixer : AssetPostprocessor
{
    void OnPostprocessModel(GameObject g)
    {
        if(assetImporter.ToString() == " (UnityEngine.FBXImporter)")
        {
            FixFBXImport(g.transform, 0);
        }
    }

    private static void FixFBXImport(Transform t, int depth)
    {
        var filter = t.GetComponent<MeshFilter>();
        bool hasMesh = filter;

        /*
         * If there is only one object in the file, it will have depth 0.
         * If there are more objects, the GameObject at depth 0 will be a non-transformed GameObject created by Unity.
         * The root objects of the file will have depth 1 then.
         * Every object that is a child of another object in the file will have depth 2 or higher.
        */

        if(depth == 0) //Root object
        {
            if(hasMesh) //If we're looking at the only object in the file
            {
                t.Rotate(90, 0, 0, Space.Self);

                var euler = t.localEulerAngles;
                t.localEulerAngles = new Vector3(-euler.x, euler.y, -euler.z);
            }
        }
        else //Children objects
        {
            if(depth == 1) //Root objects
            {
                t.Rotate(90, 0, 0, Space.Self);

                var euler = t.localEulerAngles;
                t.localEulerAngles = new Vector3(-euler.x, euler.y, -euler.z);

                var pos = t.localPosition;
                t.localPosition = new Vector3(-pos.x, pos.y, -pos.z);
            }
            else //Children of other objects
            {
                var euler = t.localEulerAngles;
                t.localEulerAngles = new Vector3(-euler.x, euler.z, euler.y);

                var pos = t.localPosition;
                t.localPosition = new Vector3(-pos.x, pos.z, pos.y);
            }
        }
        
        //Fix Children too
        foreach(Transform child in t)
        {
            FixFBXImport(child, depth + 1);
        }

        //Now for the actual mesh
        if(!hasMesh)
            return;

        var mesh = filter.sharedMesh;

        var vertices = mesh.vertices;
        var normals = mesh.normals;

        //Switch y and z axis
        var newVertices = new Vector3[mesh.vertexCount];
        var newNormals = new Vector3[mesh.vertexCount];
        for(int i = 0; i < mesh.vertexCount; ++i)
        {
            var v = vertices[i];
            var n = normals[i];

            newVertices[i] = new Vector3(v.x, v.z, v.y);
            newNormals[i] = new Vector3(n.x, n.z, n.y);
        }
        mesh.vertices = newVertices;
        mesh.normals = newNormals;

        //Fix flipped normals
        var tris = mesh.triangles;
        for(int i = 0; i < tris.Length; i += 3)
        {
            var buffer = tris[i];
            tris[i] = tris[i + 2];
            tris[i + 2] = buffer;
        }
        mesh.triangles = tris;

        //Clean up after work
        mesh.RecalculateBounds();
    }
}