Green’s Dictionary of Slang

white-shoe adj.

1. (US) immature, effeminate.

[US]J.D. Salinger Zooey in New Yorker 4 May 62/2: Phooey, I say, on all white-shoe college boys who edit their campus literary magazines. Give me an honest con man any day.
[US]N.Y. Times 22 Sept. 33/1: Monkey business as dropping simulated poison cannisters in the New York subways – the games of white-shoe boys who never grew up.

2. of the US establishment, e.g. a white-shoe law firm. [see cite 2013 for origin].

[US] (ref. to mid-1960s) B. Rodgers Queens’ Vernacular 152: cheapskate customers; nonbuyers. Syn: white-shoe trade (mid ’60s).
[US]N.Y. Mag. 5 June 14: It also [...] was a ‘white shoe’ firm, without many Jewish, black, or Hispanic partners or associates.
[US]Black Enterprise Feb. 132: Knocking at the doors of some of America's major ‘white-shoe’ law firms, armed with his newly acquired cum laude degree.
[US]N. Stephenson Cryptonomicon 664: He was just this Orange County white-shoe lawyer.
[UK]Guardian G2 30 Jan. 5/1: Nor was this some bucket-shop firm, but the bluest of the blue-chip; the whitest of the white shoe.
[US]S. Mandis What Happened to Goldman Sachs 108: Morgan was considered a ‘white shoe’ firm, referring to white buck shoes—laced white suede or buckskin shoes with red soles , which stereotypically were worn at Ivy League colleges.
[US]A. Kirzman Giuliani 26: [Y]oung men who were on track for jobs at white-shoe law firms.

In phrases

white-shoe brigade (n.) (also white-shoe boys, white shoes) [describing businessmen who prefer casual clothes to the trad. ‘uniform’ of black shoes and dark suits]

(Aus, esp. Queensland) successful rich business, typically property-developers, wheeler-dealers, etc; often linked to the wealthy supporters of Queensland premier Joh Bjelke-Petersen.

[Aus]Canberra Times (ACT) 10 May 2/5: the suspicion of the rural section to what they often unkindly term ‘the gold-chains and white-shoes brigade’ is more and more evident at party conferences.
[Aus]R.G. Barrett White Shoes 12: Do me a favour. When we get there [i.e. Queensland], knock up on the jokes about white-shoes.
[Aus]P. Temple Black Tide (2012) [ebook] He pops up now and again for the white-shoe boys [...] developers, wheeler-dealers, suchlike.
personal correspondence 25 June: The Australian use of white shoe in ‘white-shoe brigade’ differs from the American, and is insulting. Linked to fairly wide property developers, mainly in Queensland, it was based on the vulgarity of their wearing Reeboks, et al, instead of proper black shoes like father wore.