Centrists do not object to woke the theory, we object to 'woke' the verb. The end point of a fairer and more tolerant society cannot be achieved by the implementation of intolerance and bullying. A free society means exactly that, everyone is free to assert their position and everyone else is free to criticise it - that is not oppression, that is how liberal societies develop.
Objection is not oppression. Questioning is not a crime. Society moved further forward toward equal rights in the 100 years before 'wokeness' than it has in the 12 years since this particular branch of activism arrived in 2008. Viewed objectively, it's hard to see what benefit it really brings other than cementing certain subsections of society into an echo chamber, whilst also pushing centre ground liberals towrds the political right.
Whilst progressive movements begin with good intentions, their methodology evokes the opposite consequences to their intended effect. I don't think the world has become safer for women, people of colour or trans people since 'wokeness' arrived - and that is shame.
As the echo chambers become more and more vociferous and unhinged and the unelected mouthpieces for these movements become more vitriolic - more and more people will see their futility and abandon the bandwaggon. You should always keep an eye on where your movement of choice is heading tomorrow, not where it puports to be today.