With commands you can load a crossbow with entities other than arrows (such as a trident), however the crossbow will launch a arrow, not that entity.
In case you loaded a trident into the crossbow, you can see that the projectile is a trident in the crossbow's tooltip.
- Paste this command into a command block or the chat with cheats activated.
- Activate the command block or run the command.
- Hold the crossbow and fire it. (Notice the word "Trident" in the tool-tips.)
- The projectile fired will be a arrow instead of a trident.