The BBC Sport BAME Advisory Group and 5 Live Diversity Group told colleagues it was a "shocking miscalculation" and "totally inexcusable" for Vaughan to be reinstated after he was implicated in the Yorkshire CCC racism crisis last year.
The former England and Yorkshire cricketer was not used in BBC Sport's Ashes coverage last December amid the fallout from the scandal as the broadcaster felt his involvement would have represented a conflict of interest.
Former Yorkshire spinner Azeem Rafiq told MPs in November of the “inhuman” treatment he suffered during his time at Headingley, with Vaughan among a number of figures implicated in the case.
Rafiq alleged the former England captain and ex-Yorkshire team-mate had said to him and a group of players of Asian origin in 2009 that there were “too many of your lot” at Yorkshire and that “we need to do something about it”.
Vaughan has categorically denied making that comment. Rana Naved-ul-Hasan corroborated Rafiq’s claim however, as did current England player Adil Rashid.
"Michael Vaughan is implicated in this scandal and now understood to be charged by the ECB, it feels totally inexcusable that he should continue to appear, as a representative of BBC Sport," read the email from the BBC Diversity group.
"Unfortunately, that is exactly what seems to have happened. We appreciate that there are elements of detail that can't be shared about Michael Vaughan's reinstatement and that he is innocent until proven guilty.
"But surely, on a human level, it must be acknowledged how damaging, embarrassing and unsettling this is to many colleagues across BBC Sport, BBC Radio 5 Live, and the wider BBC as a whole.
"The depth of feeling (both personal and professional) and outpouring of emotion towards this decision is excruciating, overwhelming and unbearable.
"Colleagues from all backgrounds from across the BBC have been in touch to share their disbelief and dismay, with some moved to tears because of the apparent lack of empathy, understanding and leadership over this.
"What support is in place for colleagues deeply affected by this, but actually still having to work with Michael Vaughan?
"This really is a shocking miscalculation. Importantly, we would like to stress our undivided support for Lou Sutton (5 Live Sport Editor) and Steve Lyle (lead exec) who understandably are in a difficult position with this.
"We totally support them and do not want them to feel isolated or alone in this incredibly difficult situation,
"For us, this is about integrity. It's about having the integrity to stand up for what is right and to call out the ruthless calculus that prioritizes the one at the expense of the discomfort and trauma of the many.
"We are exhausted. We are tired. We are fed up of having the same discussions and reliving the same trauma. The small steps forward we make to try and build greater inclusivity and understanding are totally undone by decisions like this and that really needs to be acknowledged here."
Vaughan later apologised to Rafiq for the hurt he experienced during his time at Yorkshire. Earlier this month, Yorkshire and “a number of individuals” were charged by the England and Wales Cricket Board following an investigation into the racism allegations made by Rafiq, and the handling of those allegations by the club.
The ECB did not name any of the individuals who have been charged.