Here are a few relevant pronouncements culled from dailywritingtips.com...
The OED says
In standard English the form farther is usually preferred where the word is intended to be the comparative of far, while further is used where the notion of far is altogether absent.
It concedes, however, that “there is a large intermediate class of instances in which the choice between the two forms is arbitrary.”
According to the Online Etymology Dictionary
There is no historical basis for the notion that farther is of physical distance and further of degree or quality.
In 1926 H.W. Fowler wrote in A Dictionary of Modern English Usage
The fact is surely that hardly anyone uses the two words for different occasions; most people prefer one or the other for all purposes, and the preference of the majority is for further.
As these NGrams for advanced further/farther and further/farther advanced show, there's no significant preference based on word position, or UK/US usage. What stands out is further is always more common.
Thus, even if some people (i.e. Grammar Girl) do distinguish either the precise meanings, or the contexts in which they use each form, this is effectively irrelevant, since most of us don't. It's just pedantry.
But there are contexts where farther is never used. In "fixed expressions" such as further education (BrE for AmE continuing education), and as the verb to further (to develop or make progress in something).