He appears to be a distant relative, yes, but by my count, five generations removed from any direct connection to the banking business.
Starting with his entry [1] on thepeerage.com, a UK genealogical site for the upper classes, you can backtrack to find that his great-great grandfather was a Charles James Hoare [2], who appears, if this Wikipedia entry is the same person [3], to have been a a Church of England clergyman and himself the son of a partner in the Hoare private bank. So, C.A.R. Hoare's great-great-great grandfather was part of the bank. The four generations in between seem to have been various kinds of upper-middle class government or quasi-government employees though: clergyman, clergyman, military officer, and colonial civil servant.
Incidentally, I got the pointer to thepeerage.com from his biography in the book Reflections on the Work of C.A.R. Hoare, which calls his family background "somewhat upper-class" and references the site in a footnote.
Starting with his entry [1] on thepeerage.com, a UK genealogical site for the upper classes, you can backtrack to find that his great-great grandfather was a Charles James Hoare [2], who appears, if this Wikipedia entry is the same person [3], to have been a a Church of England clergyman and himself the son of a partner in the Hoare private bank. So, C.A.R. Hoare's great-great-great grandfather was part of the bank. The four generations in between seem to have been various kinds of upper-middle class government or quasi-government employees though: clergyman, clergyman, military officer, and colonial civil servant.
Incidentally, I got the pointer to thepeerage.com from his biography in the book Reflections on the Work of C.A.R. Hoare, which calls his family background "somewhat upper-class" and references the site in a footnote.
[1] http://thepeerage.com/p14062.htm#i140620
[2] http://thepeerage.com/p39939.htm#i399386
[3] https://en.wikipedia.org/wiki/Charles_Hoare_(priest)