Some low number M1903s are safe to shoot, some have receivers made from brittle steel that can fail catastrophically if you have an unusual event such as a case failure or an overcharged round. There is no way to tell if your receiver is OK without risking destruction of the receiver. Therefore, many people choose not to take the risk, since there are many high number M1903 available to shoot.
The quote below is from the Civilian Marksmanship Program (CMP) sales page.
https://www.milsurps.com/images/impo...0/5jwxeg-1.jpg
If the metal on your rifle hasn't been altered it would be worth restoring by obtaining a replacement stock and handguard, with the associated metal.