The culture wars were never a "distraction": they were the main event, and those who advocated ignoring them in favour of "substantive" issues failed to read the room.
In politics, what matters is winning elections. It seems absurd to have to point out something so obvious, but there it is: you have to win elections. Downplaying the conservative "war on woke" makes no sense because regardless of whether it's what the GOP is truly thinking, it's what the GOP used to win the election.
For the "anti-woke" crowd, every progressive policy success infuriated them. Years of successive social progressive successes drove them into a blinding white-hot rage. As a result, they don't just want to fight "woke": they want to burn down every social and civil institution which participated in this form of progress.
They don't care if Pete Hegseth does severe damage to the Pentagon, because they would rather sabotage the Pentagon than allow it to go "woke". They don't care if Trump's tariffs cause heavy economic damage, because they would rather lose money than let "woke" win. They don't care when people suffer and die in blue states, because those states are "woke", and anything "woke" must be destroyed.
The "war on woke" was never a side-show. It was always the main event.