Batch export selected objects from Blender to FBX

blender_batch_export.py

import bpy
import os
from copy import copy

# export to blend file location
basedir = os.path.dirname(bpy.data.filepath)

if not basedir:
  raise Exception("Blend file is not saved")

view_layer = bpy.context.view_layer

obj_active = view_layer.objects.active
selection = bpy.context.selected_objects

bpy.ops.object.select_all(action='DESELECT')

for obj in selection:

  # Capture original position in the scene
  original_location = copy(obj.location)
  obj.select_set(True)
  # Move object back to the origin
  obj.location = (0,0,0)
  
  view_layer.objects.active = obj

  name = bpy.path.clean_name(obj.name)

  if name in ["Light", "Camera"]:
      continue

  fn = os.path.join(basedir, name)

  bpy.ops.export_scene.fbx(filepath=fn + ".fbx", use_selection=True)
  obj.select_set(False)
  # reset back to original location in the scene
  obj.location = original_location
  print("written:", fn)

view_layer.objects.active = obj_active

for obj in selection:
obj.select_set(True)