If the GM decides that dear dad or whomever - the person or people the players' backstory framed as worthy folk - are in fact serial killers, than how was the character meant to carry it off? What did the player fail to do?
What action declaration or player-side resource is mean to prevent unilateral GM decisions about the backstory element?
See, there is the disconnect.
*IF* "keeping my family on the true and narrow way of good" is a vital part of the PC's concept and nature, then the PC should be actively engaged in doing that. So, at the very least, that means maintaining regular communication and visits back home, regular check-ins and insights into their daily life etc to make sure they are on the right and narrow path that will satisfy this PC that his life has meaning.
With those stated efforts (and more) the issue of "do i catch dad the serial killer and then do what my beliefs require" or "do i find out dad is having troubles and get a chance to intervene" and "do i see my sister starting to pursue dark arts and hanging with the wrong "furry" crowd" etc etc etc become no longer the mand of off-screen by both player and Gm fiat *but* become the results of challenge and success or fail - of action and results, of choices and consequences in-game.
That is why in my experience setting something like "what defines my character going forward" into some meta-only off-screen resolutions bad form. If that things is the most important thing to your character, if your character would feel such devasting loss if it turned out to not be that way at the end of some massive career as an adventurer - what in the heck were you doing off adventuring and not taking care of your biggest most foundational need?
In other words, if "what i am and who i am" is put off-screen and lockboxed - thats a poorly chosen character to be the starring role in an RPG devoted to adventuring or the like.
Again, tho, that is why we like to have the "things that matter to our characters" as well as "things that matter in the setting" be managed and handled on-screen, in-play, in-game, in-character (with a nod to occasional email exchanges and such when appropriate to resolve solo stuff that would take too long.)
At times the claims have been made that this lockboxing and backgrounding would be for stuff that doesn't matter - well - if it doesnt matter then if it is changed and not as you thought how is that a crisis?
As the examples have tended to show, when asked and queried - this practice seems not only edging into "not really off-stage and unimportant" but actually for on-screen or critical. From the *my bear does not get the wrong reactions in town* instead of chosing a large dog or other town-friendly companion (not as combat capable as a bear tho) or the motorcycle that you use to move around town being worry-proof to even the further examples of the race itself not being met with "the reactions i do not want" and now to "pleasantville family that i do not need to work to preserve or guarantee their good faith even though it is crucial to my character" it keeps coming back to can i get a meta-game eraser for these.
IMO, the first question i would have for a PC who told me "maintaining the righteousness of my other family members is the most important thing and if that fails its all been for nothing - crushed" would be "then why exactly is he going out here adventuring and not keeping closer tabs on them and their goings on? He does realize people get corrupted and suffer setbacks and fall short every day in this world, right? he does realize there are active evil forces working to corrupt people with treachery and magic, right? So, why is he an adventurer if that is actually what he cares about the most?"
In general, i find its good advice to keep the "who i am" major character GOALS tied into "on-screen" stuff, not off-screen stuff your character will not actually be interacting with.
"My character is an avid environmentalist devoted to preserving the climate especially the ice caps and glaciers."
Then why in the worlds are they signing on for a space trip to Mars and adventure?