The ability to post anon is one of the reasons this site is so successful, because it allows people a way to separate aspects of their activity here. Not everyone is comfortable showing their username on every comment or post they make. Removing that feature, even temporarily, because of a few bad actors would be disproportionately harming the majority of users with a legitimate use for it (especially given there are plenty of users who openly post the same sort of messages under their own username).
As an aside, another reason for the site's success is its relatively non-discriminate content policy. I personally feel that reactively changing that to cater to a temporary political issue would be damaging in the long term. But hey, that's just me.
E: and doesn't time make fools of us all.