This bug seems to be across all consoles and ive managed to pinpoint what causes it. In the castle settlement if raiders attack it causes the minuteman to get up from the radio, and without loading a save he WILL NOT SIT BACK DOWN. It seems as though since it doesnt have man power it isnt turned on, keeping the npc in a paradoxical loop of "i need to work the radio but i cant sit down until its powered on, but to power it on somebody must be sitting at it." Ive exausted all of my efforts on finding a fix and now it is up to you bethesda to solve this issue. If i had to make a suggestion, i would say either:
A.) Make the minuteman on the radio a normal minuteman so you can reassign him his spot (give him a special name like radio host)
B.) Allow anybody to broadcast. The only downside to this is that it will always be the same voice on the radio regardless of who you assign