Play to the whistle has always been installed in you from when you first play the game, Sheffield United players just stopped when the lino raised his flag, Shelvey rightly carried on, & it wasn't offside in the first place, Carroll was just onside.
I believe the refs have been instructed to let play go on if the lino raises his flag, & let VAR sort it out should the player put the ball into the net, apparently players & coaches/managers have been told this as well.
Pre- VAR, the offside flag being raised [rightly or wrongly] was usually a pretty conclusive event and few [if any] referees would override their linesmen. Now however, that flag is simply an indicator, a suggestion or a recommendation, and referees can afford to ignore it and let VAR sort out that phase of play if it continues. Sheffield UTD were extremely naive to take their lead off the linesman's flag last night because the flag itself has NEVER been solidly conclusive, it's just always
seemed that way due to referee solidarity with their linesmen, through "good" decisions or "bad."
Now however, attackers who continue to play on and who get goals in doing so will likely force VAR to take a look.... and this may become the case even if the referee has blown for an offside. If however, this occurs and VAR refuses to intercede, because they simply wish to re-enforce the authority of the ref's whistle, then they'll find themselves having to make a decision.
Are they employing VAR to accurately enforce the laws of the game, or are they using it [or sometimes NOT using it] to protect the referee's authority? If a situation arose where a player continues a phase of play "against" the ref's whistle, would VAR ever validate this, basically saying that in some instances, the whistle itself was wrongly blown?
Or does the ref's whistle trump ALL VAR scrutiny once it's been blown, rendering any player who ignores it as warranting a card?