No. 95-5393: Friends of the Vietnam Veterans Memorial v. Kennedy

In Friends, the court relied on 16 U.S.C 1.1.1 to uphold regulation of sales of t-shirts, and also the regulation of demonstrations, in the National Capital Region:
But Congress has charged the National Park Service with regulating the use of the Mall so as to “conform” such use “to the fundamental purpose” of “conserv [ing] the scenery and the natural and historic objects ․ and ․ provid[ing] for the enjoyment of the same in such manner ․ as will leave them unimpaired for the enjoyment of future generations.”  16 U.S.C. § 1 (1994).   To this end, the Park Service has promulgated regulations providing that “[d]emonstrations and special events may be held only pursuant to a permit issued” by the Park Service. 
[link to Friends]
These Park Service Regulations for the Capital Region are CFR Title 36 Chapter 1, Part 7.96.  [Link to 36CFR 7.96]
7.96 (g)(1)(i) unmistakably refers to the First Amendment:
The term demonstrations includes … all ... forms of conduct which involve the communication … of grievances... 
This constrains the First Amendment to fit within the mission of the National Park Service.

The Rule Analysis of the October 2010 change to the definition of demonstration in 36 CFR 2.51, noted on page 64149 of the Federal Register Vol 75 No 201, makes clear the intent was to allow minor dissent: it allows the wearing of t-shirts, caps, and tattoos by individuals.