I'm not really sure what is meant by conservatives being at the forefront of rushing to cancel people, but as someone extremely to the left, it seems like more democrats/liberals are the most eager to cancel them!!!! immediately.
I don't really care who is A or B list or how one determines who fits into which category, but the bottom lime from my viewpoint is that the majority of the population cannot keep an open mind about situations (or otherwise wait for facts) and will immediately rush to judgment based on how they feel or how it benefits them. Look at the Biden sexual assault scandal that came up just prior to the election. Many people were very quick to dismiss his accuser, even before further details about her came out. Or maybe moreso than dismissing her, they tried to ignore it because they needed Biden to win the election and not Trump. Then you have other cases where there's absolutely zero known about the man being accused and there are tons of 'OMG this is the problem when you don't believe the accuser!!!!' replies when people aren't quick to rush to judgment. So it's all just situational, no matter how much one thinks they are equally applying their social justice skills.