I think you're basically correct OP, but specifically, I imagine Republicans are afraid because of the perception that the Dems are shifting to appease the far left minority ultra-woke Twitter crowd, and this fear is amplified in the primary season where to a certain extent you need to pander to the extremes.
But it's not a blanked fear, and depending on the eventual nominee it could dissipate. Biden is easy to ridicule, but isn't very frightening. Tulsi Gabbard will never be the nominee, but she's not a candidate that would evoke much fear for right leaning individuals at all. Even Yang, who is in some ways more economically left than the rest, isn't that frightening because he comes across as this authentic somewhat socially awkward, well-meaning nerd. That last thing from an evangelical leftist.
But the thing is that we're stuck in a positive feedback loop. The right goes further right, the left gets angry and goes further left, the right gets angry and goes further right, and so on. I don't care who is to blame for starting it... but it needs to end. Both teams need to start looking at more moderate candidates, not ones with religious zeal, not ones that fire up the base. And it's not even really so much about policy as much as it is about presentation and perception. The alternative is that we'll forever be divided and at each other's throats.