The problem with centrism is that some people like to see it as the only inherently sensible position, filled with rational and level-headed people who would do a great job of running the country if only they were given the chance, unlike the entrenched extremists on the left and right.
But take a gander through Twitter and you'll find that's not the case - many centrists (to use the term broadly) are just as hysterical, ideologically minded and entrenched as their counterparts on the left and right. I sympathise with the wider motivations of a lot of the People's Vote types but a lot of them are incredibly hysterical and over-dramatic at times, no less so than the worst of Corbyn's fans.
A lot of this comes down to Blair - the popular view is often that he was an unprincipled pragmatist who veered to the centre because he had to. That's entirely incorrect, he was a deeply ideological position with a very fixed and entrenched worldview of his own. Whether that ideological was good or not is another debate but he was by no means someone who liked compromise and he wasn't necessarily pragmatic either. He simply did a good job of convincing everyone else he was.