The thing is, when you actually ask someone who claims to consider continuity sacred what they mean, they typically refer to a particular take on the character that itself contradicts previous takes. Michelinie and Layton, whom some on this board treat as golden sacred cows, themselves contradicted bronze and silver age writers and even contradicted themselves between their first and second runs. So this supposed "continuity" obsession is a lie. It's a lie born of trying to bring the weight of history and tradition to what is really just a simple expression of a preference for a particular take.
Moreover, when writers attempt to reconcile continuity, the result is typically a dry, awkward, mess. A story or at least a chunk of a story that is just a big No-Prize, trying to neaten continuity that is so contradictory that it can only be neatened by the most tortured of Frankenstein stitching. The result lacks any entertainment value, because all it is is a big No-Prize pretending to be a story.
Now that's not to say I despise old continuity. For example, I prefer Silver/Bronze age Mandarin to what he mostly became from the eighties onward. I still think that that little five page origin story Stan Lee wrote for him was the best Mandarin story ever, combining the pathos of tortured aristocrats like Roman Sionis and a tortured super-soldier like X-23 with the disturbing exploitation of Christopher Columbus.
But I prefer that simply because I think the take Stan Lee had on the character was the best, not because I think Silver Age continuity is inherently sacred.
It has gravitas. It means what the characters do and what happens to them have meaning. When you ignore continuity...nothing really matters. It's like serial versus episodic.
If the choices a character makes has ZERO lasting effect or meaning...you lose interest. Why should Cap care that the Red Skull killed Buckey and so many people...ehhh...hes a nice guy for no reason all of a sudden and all those dead people mean nothing.
I don't mean be a slave to it...but it builds the world the universe...the other way feels like a petulant child kicking over a sand castle.
Not saying you don't have a point on people may prefer certain areas/eras of continuity.