Except it's not up to you in Fallout 4. The game outright tells you how you need to feel about the McGuffin, the protagonist spends the first half of the game running around the wasteland whining about his lost child and telling people about how he or she misses them so much, and while that makes sense given that they are the child's parent - it's needlessly restrictive for the player. If you're writing a story for a freeform RPG like Fallout, and it doesn't make sense for the protagonist to be anything but an emotional wreck who desperately wants to find what they're looking for, you should probably go back to the drawing board.
The difference between Fallout 1, 2, New Vegas and Fallout 4 is that the former three never forced the protagonist to feel anything towards the McGuffin beyond their obligation to find it, it was just your character's motivation for leaving their former life behind, and interacting with the world. They had to find that initial objective, but you never saw the Vault Dweller crying about the Water Chip, or the Courier whining about the Platinum Chip - they just asked people if they knew where to find what they were looking for. Their feelings towards the McGuffin, and their mission, were completely up to you.