One of the reasons that (general) political view declarations are important, and persist, is because they play a key role in aiding the interpretation of what is being said. Of course what is said, often strongly implies such a declaration, but not always; that's why it becomes useful to declare "what side one is on", even when one wishes to remain neutral (until one's understanding of the issue at hand has matured), unless one is prepared to have their utterances treated with suspicion. This is a more general phenomenon, not only restricted to political views, but I believe that politics makes the phenomenon more pronounced. Much more could be said about this, but here I'll just give an example, which illustrates the idea. I will use an abstract example (to avoid the risk of creating a distraction).
Let the context be one where there is a stark divide in views regarding some issue in it. Now, say there's a proposition 'A' that expresses an attitude regarding that issue in the mentioned context. That is, some would think, and feel very strongly that A, whereas others would think, and feel very strongly that not A.
Person 1: "A"
Undeclared: "Of course"
Person 1: "Not A"
Undeclared: "Of course"
In both cases, it's very likely that Person 1 (or person 2) will inquire "what do you mean?" And why are they doing this? Was the Undeclared's statement not clear enough? It was, but coming from an Undeclared it may be taken as meaning the opposite of what it says, e.g. being a sarcastic remark; the existence of such remarks, being common where political views clash, adds to the ambiguity of the actual intended content of undeclared's statements. The degree of this phenomenon, I suspect, would be a function of the context's scope, i.e. given some context, what is the extent of the Undeclared's lack of declaration.
Needless to say, this leaves those who wish to maintain neutrality (which is more often than not the wise attitude, I believe) in an uncomfortable position of their opinions being either notoriously misunderstood or treated with suspicion, so there exists a pressure to declare oneself politically, even if one is neutral. In a "war of words", which often is the form of political discourse outside of echo chambers, being declared facilitates unpacking the non-explicit, intended content of the actual statements that are made. So enhancing one's clarity is a tempting reward for the mere cost of an instrumental declaration (even when it is inconsistent with one's actual view). Consequently, this mechanism inadvertently facilitates the proliferation and sustainment of extreme views, at the cost of the more balanced ones.