Alluding to the former practice of binding government documents in red-colored tape. First use appears c. 1658 in the publication Public Intelligencer. See cite below.
1884, Eliezer Edwards, Words, Facts and Phrases ...curious, Quaint and Out-of-the Way Matters, page 469:
The use of red tape for tying up papers is of considerable antiquity. An advertisement in the Public Intelligencer, December 6, 1658, offers the reward for a restoration of a 'A little bundle of papers tied with a red tape, were lost on Friday last was a sevennight, between Worcester House and Lincoln's Inn.
At twilight in the summer there is never anybody to fear—man, woman, or cat—in the chambers and at that hour the mice come out. They do not eat parchment or foolscap or red tape, but they eat the luncheon crumbs.
All the red tape and paperwork that goes on there prevents any progress.
1979, United States Senate, Committee on Finance, Crude Oil Tax, U.S. Government Printing Office:
That committee does not cut through red tape; it merely provides better scheduling for different agencies so you do not have sequential review by different agencies , so that you have some kind of simultaneity in the review by different agencies.
One conspicuous cost of the compromise reached was a promise made by Senator Chuck Schumer to Manchin on what was vaguely called permitting reform: a catchall phrase referring to a whole host of efforts to cut red tape and ease the rollout of energy infrastructure.
2023 June 23, Jonathan Freedland, “With even leavers regretting Brexit, there’s one path back to rejoining the EU”, in The Guardian, →ISSN:
They said we’d be free of all that tedious European red tape and would take back control of our borders, encouraging anyone agitated by immigration to believe that fewer people would come in. […] Post-Brexit red tape is strangling thousands of small businesses, whether travelling musicians or exporters of goods, tying them up in daunting forms or extra charges that cost time and money they don’t have.
Usage notes
For the figurative sense of bureaucratic procedures, the metaphor is often extended, e.g. cutting [through] red tape, bound up in red tape.