The bai in baizuo is also from baichi, which means idiot. So, baizuo doesn’t just mean white left but also idiotic left. A more fitting translation of baizuo would be white leftoid or white left*rd.
That’s not how Chinese language works. Just because 白 (bái) can be part of a word that means “idiot” doesn’t mean that it is infused with the meaning of idiocy. That’s like saying “the bai in baizuo is also from mingbai, which means clear/reasonable so baizuo doesn’t just mean white left but also reasonable left”. Which is obviously absurd lol. In most contexts, 白 means “white” and nothing else, although there are obviously many cultural associations with the colour white that are layered on top of that.
Is this your hypothesis or did you read this somewhere? The wiki article in the OP says 是”白人”与“左派”两个标签结合组成的称号, i.e., it’s a grouping of “white person” and “left wing”. I’m not saying you’re wrong, it’s just that I didn’t get that vibe as someone who speaks Chinese, especially because 白痴 is more of a clinical/bookish term for idiot and not something I heard people say very often in everyday life. I only went to uni in China and I’m not a native speaker though.