It is called a "Dog Bone"
It is a weight mounted with rubber bushings to absorb NVH (Noise/vibration/harshness).
It can be removed with no real issues. It weights about 15 lbs.
When I ran my own Mustang performance shop, I removed dozens and dozens of them and no one complained.
Except that one guy who found out 6 months after the fact and wanted it put back on. For no other reason than the factory thought that it should be there. Even though he could not discern and difference in the vehicle with or without it.
My premise is, if you can not tell the difference, why pack 15 lbs of extra weight around?
The driveshaft is often a source of vibrations, and when it's straight, balanced, and the pinion angle is set right, you can still get harmonic vibration at certain speeds due to the interaction of various parts' natural harmonic frequencies. I've always removed mine and chunked them. But, if I ever did again, I'd keep mine for a just-in-case kinda situation. It would've been nice to try reinstalling one when I was having vibration issues.
I would put the car together and run it down the road for a bit. Remove the dogbone and see if there is a difference for ya. If not, shelf it for a case where you might need one.