Far as I can tell most people that are off-put by Fallout 4's story are bothered by the family dynamic at the beginning and, though many love to argue that it's fine, they have good reason. Let's take a look at the provided backstory of protagonitsts in previous fallout and Bethesda games.
Fallout 1: The vault dweller, sent into the wastes to find a new water chip. Backstory? You came from Vault 13.
Fallout 2: The chosen one, sent out to find a GECK. Backstory? You're the vault dweller's grandchild and come from the tribal village of Arroyo.
Fallout Tactics (Beth doesn't consider this canon even though it is occasionally referenced): The warrior, you are recruited to the BoS and fight several factions in the midwest. Backstory? You're a tribal from the midwest.
Fallout 3: The lone wanderer, escapes the vault when his/her father leaves and everyone turns hostile. Backstory? Your mother died in childbirth, your father is a doctor and scientist working on water treatment. You are a teenager, no matter what.
Fallout New Vegas: The courier, shot in the head while delivering a package, on a personal mission to find out why, if not to seek revenge. Backstory? You worked as a courier and at some point in the past carried a package with nuclear detonation codes. Other options come up in the game, but the player decides which are true.
The Elder Scrolls: Arena: The eternal champion. Imprisoned by Jagar Tharn, you escape and fight to take him down. Backstory? You were once the head of the Emperor's guard. This character was completely open when the game was released, but has since been set as a male named Talin, presumably for use in lore.
The Elder Scrolls II: Daggerfall: The hero of daggerfall, recruited by the emperor to investigate the king of daggerfall's death. Backstory? You were once a prisoner during the events of Arena. The emperor released and pardoned you, seeing potential as an agent of the blades.
The Elder Scrolls III: Morrowind: The nerevarine, sent to morrowind in hopes of fulfilling a prophecy and defeating Dagoth Ur. Backstory? You are sent to morrowind against your will, possibly an imperial prisoner before being selected.
The Elder Scrolls IV: Oblivion: The champion of cyrodiil, gets caught up in a quest to replace the assassinated emperor and close the portals to oblivion. Backstory? You are an imperial prisoner given a chance to escape when the emperor fled assassins through your cell.
The Elder Scrolls V: Skyrim: The dovahkiin, discovers they possess the soul of a dragon and are the only one who can drive the dragons back out of tamriel. Backstory? You were captured by the imperials near the border of skyrim, they think you are part of an opposed military group.
Now Fallout 4: The sole survivor, emerges from the vault after 200 years, motivation unknown. Backstory? You are married, to the opposite six. You have a male child named Shaun. You are potentially a military veteran (listen to dialogue at beginning of character creation).
Which of those games most restricts your imagination when filling in the blanks about your character? Answer: Fallout 4, followed by Fallout 3. Did Bethesda decide to get a new lead writer? They could have at least made you a single parent, leaving things a bit more open. I definitely see a reason to be off-put by this change, especially for the role-players of the fandom. When you come to expect a ROLE PLAYING game where you actually get to make up your own role, forcing a particular role can be anger-inducing. Imaging playing a tabletop where you've grown really invested in a character and come up with a cool backstory, and your game master blows it out the window in the first few seconds by saying all the PCs are siblings, or assigning them all spouses.
I will play Fallout 4, I'll play the [censored] out of it, but I fully understand why people are angered by this story decision.