It’s a simple bit of civics:
 
“You can pick your friends, and you can pick your nose, but you can’t pick your friends’ noses.”
 
The silly saying has an unknown origin. “You can pick your friends and you can pick your nose—but you can’t wipe your friends on your trousers” was cited in an Indiana newspaper in 1969. “You can pick your friends, and you can pick your nose, but you can’t pick your friends’ noses” was cited in a Michigan newspaper in 1971.
 
 
3 April 1969, Tri-State Triangle (Angola, IN), “Dumpers Dialog” by Lee Greenfield, pg. 2, col. 4:
Ahh, dear me…I have all of a sudden recalled a nasty expression which I heard from an obscure friend, and, with the editor’s kind permission, it shall here and now be gotten out of my mind and onto this page: “You can pick your friends and you can pick your nose—but you can’t wipe your friends on your trousers”.
 
Google News Archive
26 March 1971, The Michigan Daily (Ann Arbor, MI), pg. 10, col. 6 ad:
SOUTH QUAD Presents
THE MOTOR CITY MUTANTS
REVUE
“You can pick your friends, and you can pick your nose, but you can’t pick your friends’ noses.”
 
12 September 1974, Moulton (IA) Weekly Tribune, “Grapevine,” pg. 2, col. 1:
Betty O., you can pick your friends, and you can pick your nose, but you can’t pick your friends nose!!!!
 
Google Books
National Lampoon
1974
Pg. 61:
“You can pick your friends, and you can pick your nose, but you can’t pick your friend’s nose.”—Benjamin Franklin
 
14 May 1976, The Colt (Arlington High School, Arlington, TX), pg. 2, col. 3:
Hope you all have a nice summer, and maybe you will if you just follow this advice: You can pick your friends and you can pick your nose, but you can’t pick your friends’ noses.—Chad Goetz
 
IMDb (The Internet Movie Database)
Over-Under Sideways-Down (1977)
ROY: Cosmo, you can pick your friends, and you can pick your nose, but you can’t pick your friends’ noses.
 
Google Books
The Hand Book:
Interpreting Handshakes, Gestures, Power Signals, and Sexual Signs
By Linda Lee and James Charlton
Englewood Cliffs, NJ: Prentice-Hall
1980
Pg. 81:
Remember that little ditty:
 
You can pick your friends and you can pick your nose but you can’t pick your friend’s nose.
 
Nor can you pick your own nose in the presence of your friend.
 
OCLC WorldCat record
More gross jokes
Author: Buck Jones; Deena Fleming; Tangerine Press (Firm)
Publisher: New York : Tangerine Press, ©2005.
Edition/Format:   Print book : Juvenile audience : English
Database: WorldCat
Summary:
“You can pick your friends, and you can pick your nose - but whatever you do - don’t pick your friend’s nose! Packed with hundreds of jokes thath are as gross as they are fun, this hilarious book will have you - hahaha, plunk - laughing your head off”—Page 2 of cover.