Both Biden and Bloomberg, aged 77 and 78 years old respectively, have lived long lives, lives that spanned across years of systemic sexism and racism. They have overseen the existence of legal discrimination against minorities where sexist or racist actions or words were accepted and even encouraged. This means that even just due to a product of the climate of the era, these men have probably done some questionable things.
But the thing is, their problem isn't a "shady" history, but the fact is that they cannot acknowledge and apologize for any mistakes they have made.
Bloomberg very clearly exhibited this lack of humility in his first debate yesterday. When asked about previous hostile work environment allegations by female workers who were made to sign nondisclosure agreements, instead of acknowledging any of his possible transgression, he double backed on the supposed fact that "both parties" did not want to talk about it. If you ask me, those NDAs likely contain very damaging allegations against Bloomberg, just how many businessmen of the past, including our Cheeto-in-chief, are guilty of such sexism. However, what makes Bloomberg comparable to Trump is not that he has done anything bad, but the fact that he will not apologize for it or even say that his sexist mindset has changed.
Furthermore, when approached about his stop-and-frisk policy, Bloomberg did not apologize for the racist intent behind the method but only apologized for the outcome, feigning that he did not know what such a policy would entail. America is racist now and definitely was racist at the time of stop-and-frisk so for Bloomberg to pretend to not understand the implications behind the policy — that minorities would be singled out discriminatorily — is just insulting and ridiculous.
Biden has demonstrated the same immovable quality. For example, when Kamala Harris confronted former Vice President Biden on his questionable policies on bussing in the '70s, which personally affected the education of Harris, Biden responded with no humility, refusing to apologize and stated that he regretted nothing. This was at a level even greater than Bloomberg's citywide stop-and-frisk method, and Biden could not even apologize for this.
It is well understood that the boomers experienced an era where discrimination was widely accepted and for a while that was all they knew, so it is to be expected that their mindset was shaped by that age, at least initially. It is OK for them to have made mistakes in the past but what is not ok is that they refuse to be held accountable for their mistakes. Their responses to these accusations serve to justify that most baby boomers are stringent in their ideals, no matter how wrong they are, refusing to adapt to the times — and that is not a quality that we want in a president.