I think my most unusual headcanon is a pretty dark one (obligatory queerphobia/homophobia warning). It's that D-class aren't always death row inmates, but the foundation wants its employees to THINK that they are all violent criminals, for convenience, and by taking this to its natural conclusion, the foundation's roster of D-class is largely made up of orphaned children, isolated/lonely people and people who were sentenced to death for being queer, as well as anyone. The last example is the one that I have extrapolated the most extensively upon (being queer myself).
Anyone who forms any notable emotional relationship with (one or multiple) D-class must therefore be terminated, transferred or amnesticised (depending on the importance of the person in question), in order to hide this secret and prevent an uproar. The foundation still wears a rainbow in June - in the most horrific version of 'corporate' greed possible; distracting queer employees from the foundation's violations of human rights.
(Yes, this does mean that I decided, for fun, that I would create a universe where queer employees of the foundation are forced, without their knowledge, to perpetuate queerphobia by killing their fellow queer person. It's for that existential horror high.)
I just think that it's totally natural for the foundation to exclusively be an LGBTQ+ ally when it conveniences them and saves money or resources. They would only punish queerphobic employees if the LGBTQ+ employees and allies outnumbered them, as an extension to the previous headcanon.