She is neither in my jurisdiction or line of work but I would not instruct her. Her complaint is valid but I think her way of dealing with it isn't.
She is considering reporting him to the Solicitors Regulatory Authority. This incident might have merited a report on the basis of failure to consider equality/diversity had she gone to them first. Having once had a (utterly spurious) complaint made by an aggrieved client against me and my then boss I can tell you it's a very unpleasant situation to be in. I remember being physically sick the day the letter appeared unannounced on my desk. Waiting for their decision, despite reassurance from my much older and experienced boss that the complaint would be rejected, was awful.
Now what are they going to do? Suggest diversity training? The shock of having a complaint made won't exist.
If he were a partner in my firm we would not be happy with him at all and he would probably be hauled over the coals by the management and be sent on compulsory diversity and equality training. I don't think it would be a resigning issue if this were a one-off incident (although for any firm which provides advice to public sector/ government agencies there is likely to be a need to do some explaining and confirming to such clients that the firm understands diversity and equality and has a policy which they apply. This incident would count against a firm in a public sector tender)
If he were an employee it would be a disciplinary and training issue but not a dismissal , unless there were previous warnings.
If she were an solicitor, rather than a barrister, whether partner or employee I would not be happy with the way she handled this. I discussed this with 2 of my female partners and a female employee all of whom thought he was out of order but so was her response. However she is self-employed and it's up to her.