So a client of a professional firm "is entitled to" exercise a veto on their hiring decisions?
What do you think would happen?
No. You hire whomsoever you accept responsibility for hiring.
But if the hiree is to handle clients' accounts, then they are entitled to the same professionalism as would be extended by the capturing (sorry about this term, maybe you have a better one) partner of that firm.
Looking at your scenario of a solicitors or accountants firm in a small town, this means that, before hire, one of the senior partners would explain and lay down the law about professional treatment of clients and the confidentiality of their information. It being a small town, it's likely that the senior partners would realise that if one of their clients and one of their staff were inimical, either that staff member would be kept away from any data of that client or a hint dropped to the client about his/her nemesis being now working at the firm: that's their cue to jump ship. Keeping the client in the dark would be setting a time-bomb.
This situation is far from 100% secure but it has built-in penalties for someone abusing information gained via the nature of their job.
When doctors, dentists, etc retire and advise ex-patients that they intend - unless otherwise advised by any patient wishing to go elsewhere - to forward patient records to Dr Welby nearby, they are doing pretty much as outlined above. At least those that advise their patients do.
But openly advertised buying and selling of "blocks" of clients between accountants without the clients having any say in their "transfers" is quite wrong and unfair to the clients concerned. They signed up to have legal/financial services done for them, no more.