In what year, or by what rule change, was the practice of leaving
outfielder's gloves on the field while their team was at bat
abandoned, or prohibited?

Hello.

From the web site Hickoksports.com:

"The following rule was adopted in 1954:

Members of the offensive team shall carry all gloves and other
equipment off the field and to the dugout while their team is at bat.
No equipment shall be left lying on the field, either in fair or foul
territory.
So 1953 was the last year it was legal...
BTW, if some skeptic wants written proof, you can find this on Page
2295 of Total Baseball (1993 edition)."
http://www.hickoksports.com/history/qbas0001.shtml

Another source: Allentown Allnighters web page
"It was 1954! In the majors, one rule change took place....players
were no longer allowed to leave their gloves on the field between
innnings."
http://continuinglg.50megs.com/all.html

The 1954 rule change is codified as Baseball Rule # 3.14
See The Complete Rule Book on this tripod web page:
http://members.tripod.com/bb_catchers/catchers/rulesall.htm

search strategy: "their gloves on the field"

I hope this helps.

I appreciate having references to authoritative sources.