The sentence in text still reads ambiguously. It still reads like a hypothetical, "insisting that mentioning both sides makes you some kind of enlightened centerist" implies that the people insisting that it makes you a centerist above it all, is what pissed you off. I know english is a stupid language but I clearly wasn't the only one that thought you were upset about the people calling them spineless centrists and not the people doing the spineless centerism, particularly implies that "mentioning both sides makes you some kind of" implies there is ever a time it does not. Hope that clarifies where the structural issue lies with the wording.