Phase transitions and bifurcations show up all the time in natural systems, from mathematics to cell division and population ecology; I don't know why people think social structures would be immune from this.
You're right but because it's no different from someone saying their specific solution is the only way. In reality, there are a multitude of different opinions and it seems likely to me that more than one would be effective.
> There's some times and things where one should expect a normal distribution, and other times and things where a binomial distribution shows up.
Sure things might tend to distribute into two major positions but that doesn't mean nobody holds a different opinion and it says absolutely nothing toward whether those two solutions are somehow the ideal solutions (or one of them, in the case of the OP).
Your statistical example actually takes things the wrong direction. The person you are responding to is positing a distribution with more than two modes, not fewer, and by suggesting there are two your example actually is closer to the “centrist” straw man.
The argument you are calling “centrist” is not claiming there is a “truth somewhere in the middle”. It’s claiming there are plausible positions (concentrations of probability in your metaphor) in more than just two locations.
I also considered adding that the assumption of a one-dimensional parameter space is also overly reductionist and not representative of the majority of positions people take when they feel like the mainstream choices are both wrong.