Rabbatts described the FA's handling of the Carneiro case as "seriously disappointing" after the organisation failed to take action against Chelsea manager Jose Mourinho over his touchline spat with the doctor in August.
The IAB's independent members have written a joint letter to FA chairman Greg Dyke, who has said Mourinho should apologise to Carneiro, and all FA councillors backing Rabbatts and criticising the investigation.
"The FA Inclusion Advisory Board members have expressed deep concerns about a number of recent anti-discrimination cases," British media reported the letter as stating.
"We are looking forward to meeting with (chief executive) Martin Glenn and (director of governance) Darren Bailey to discuss these issues in more depth and in the hope we can continue to support the FA and its values to see inclusion and diversity developed across the game.
"In the meantime we wish to express our unwavering support for Heather Rabbatts and further, to seek reassurance that she still has the full support of the FA board," read the letter.
"We were concerned to see two members of the FA Council question Heather's integrity this week with an FA enquiry now underway. Their seeming priorities surely serve only to distract from the real issues at stake within football such as fairness, equality and respect.
"We would question whether Heather Rabbatts has any charge to answer to and therefore the IAB calls for this matter to be concluded promptly so that she can continue unhindered in her many good works at the FA IAB helm and as a member of the FA board."
Former Chelsea player and independent IAB member Graeme Le Saux previously said Mourinho's dispute with Carneiro had tarnished the game's reputation and set the FA's efforts to change the sport's culture back 30 years.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Tony Jimenez)
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