I think one of the major issues that anti-woke media has is that, to be blunt, they're lazy. I can't count the number of people I see on places like Youtube who start criticizing woke trends and get decent followings, then let it completely go to their heads and begin swinging furiously at windmills. They become caricatures of everything they claim to be against. It's just like how media outlets would attack Trump for absolutely ludicrous things that were obviously untrue, while blissfully ignoring more fundamental faults with his presidency that required them to actually dig a tiny bit to get the full details on.
What I'd do is take a systematic approach that first highlights how different things used to be, because a lot of people simply don't remember an era before all this was normalized. Talk to older people - on both sides of the political spectrum - and ask them their opinions, then find younger people who agree with them. Construct a strong narrative on unbiased data and acknowledge the argument of the opposition. If you ignore them, they'll just call you out for things you never said. But if you take a reasonable approach and address common criticisms, especially if you go 'we admit there are things we need to improve on as well', then they'll be baying and foaming at the mouth with the most irrational and absurdist takes imaginable. I see it on history channels a lot. The moment you start using communist records and literature against them, they absolutely lose their shit and go on truly epic tantrums that turn moderates against them in record time.