I find this idea to be honestly laughable, especially from an American. What's really happening here is pretty simple. You have a guy whose maybe an average amount bigoted, a little but not much. He spends years voting for the Democrat party and supporting Democrats because he is told that doing otherwise means he is bigoted. The issue he has is that he has the aforementioned bigoted views. When he expresses, say a general distrust of trans people, he is condemned as a bigot. So he is faced with two options: change his mind (hard) or deny reality (easy). So he claims that the left used to be distrustful of trans people like he is, but now has changed to be "woke" in accepting them. What really happened is that he discovered he had right-wing views on these matters and that the left did not. This fantasy that the whole world has moved around him, instead of him moving within it, is simply a way to rationalise his beliefs. He is right-wing, but embarrassed about it.
This is quite a common view throughout history. A good example would be the "moderate" white during the civil rights era, who wasn't racist but paradoxically opposed equal rights laws. The world is filled with people who wish to appear progressive, yet do not want to do the often difficult introspection required to embody that belief system. They would like to be seen as a tolerant person without having to let go of their intolerant views.
You need only read a few of this man's tweets to see that he has drifted to the right, along with much of America. Perhaps he always thought like this and just hid it better before. He is, for instance, advocating the abolition of trans healthcare for minors. The Democratic party has never held this view or anything approximating it, yet he claims with this comic it used to be a "centre left" position. Another great tweet that almost entirely disproves his narrative is one where he talks to the white nationalists in his replies. He obviously condemns them as trash, but fails to realise that being regularly exposed to white nationalists who support the same candidate as you is a definite sign of a political shift. It is clearly not something that would have happened to him before and is clearly not the left running away from him, but him running towards white nationalism. He frequently makes tweets mocking peer reviews papers, an anti-intellectual bent which I'm sure he would not have expressed before.
You can see his progress clear as day. He used to be "neutral" on the issue of trans rights (thinking both sides are bad), now he opposes trans rights. He is currently "neutral" on the issue of race (thinking both racists and anti-racists are bad because anti-racism acknowledges that black people deserve help in society which is racist), eventually he will be openly racist. This kinds of both-sides centrism is really just intellectual frailty. Instead of considering the points made, they just point out the aesthetics of the movements and use that to ignore them. "BLM has riots, racists have riots, therefore they are the same and I'm superior to both and they're both wrong." Of course, when you place yourself at the midpoint between people who want equality and people who are racist, you are a moderate racist and not a moderate civil rights activist.