About doctor's practices: ACD's own early experience trying to set up in practice as a new GP showed him that the *historic reputation* of an existing practice was very important - and that that of an established one tended to be strong whatever the actual quality of the treatment. Personal connections meant a lot more than skill, unsurprising given that there was little effective in practice that Victorian doctors could do for their patients for many illnesses beyond diagnosis and palliatives.
People therefore tended to attend the same practice for years, and only gradually moved to an alternative.

Compare Percy Trevelyan - no money, no swish office, no established connections, and all the skill in the world wasn't enough to bring in patients.

And I am afraid both Pycroft and ACD *were* very much being anti-Semitic, in that underhand, sneery way that is still too common in Britain - largely out of jealousy towards rich and successful members of the Jewish community.

These stories were written in the 19th century. Overt racism was acceptable then in a way it isn't now (but even so, you still see it), and overt racism is scattered all over them. ACD was racist. We can't avoid it, indeed it would have been astonishing if he wasn't. OTOH he exhibited some self-awareness that this was the case, and tried to strive for fairness in his personal dealings.