I think the answer to the headline question is "not very, which is why everyone thought Cavendish was a bit weird" :-)
But focusing on the detailed question - from his entry in the revised 2004 Oxford Dictionary of National Biography:
Almost misanthropic in his reserve, Cavendish never received strangers at his residence, and ordered his dinner by leaving a note on the hall table. He seems to have had no other communication with any of his female domestic staff.
The original 1886 edition has it as:
He received no stranger at his residence, he ordered his dinner daily by a note left on the hall table, and from his morbid shyness he objected to any communication with his female domestics.
This seems to clarify it as "he wrote one note per day requesting his meals, and otherwise ignored his female staff". Which implies a bit less communication than the way Wikipedia (and Ley) phrase it, and certainly makes it likely that only the housekeeper would actually be expected to read the notes.
Having said that, literacy was not that uncommon even among the working classes, and it is not a particular stretch to assume the maids could read as well. By 1800, an estimated 40% of women in England and Wales could read and write (compared to 60% of men). These rates were higher in London than in the national average; in a 1760s sample of emigrating servants, the London group were about ten percentage points more likely to be literate than those from elsewhere in the country. It would presumably also be more likely among younger women than older, given the gradual increase in education rates.
So I think it is entirely plausible that the majority of his household staff would be able to read, especially if he had deliberately wanted to have a literate household - it wouldn't have been that difficult to hire qualified people - but in the case of this particular situation, it probably wasn't needed.