To determine the clinical setting where extensive surgical debridement, decompression, or amputation is not indicated, we need to understand each condition given in the options:

1. Progressive Synergistic Gangrene: This condition involves rapid spreading tissue death caused by bacterial infection, which requires immediate surgical intervention to remove necrotic tissue and prevent further spread. Thus, extensive surgical intervention is warranted.
2. Acute Thrombophlebitis: This condition is characterized by inflammation and clot formation in a vein, usually superficial, and is typically managed with conservative measures such as rest, warm compresses, and anti-inflammatory medications. Surgical intervention is not generally indicated unless there are complications like a clot propagation that can't be managed otherwise.
3. Acute Haemolytic Streptococcal Cellulitis: This bacterial infection spreads rapidly under the skin, often causing severe local and systemic symptoms. In cases where rapid progression or necrotizing fasciitis symptoms are seen, extensive surgical intervention may be necessary.
4. Acute Rhabdomyolysis: This is a condition involving muscle breakdown and release of myoglobin into the bloodstream. While it primarily requires medical management such as fluid resuscitation to prevent kidney damage, surgical intervention may be necessary if there are compartment syndrome manifestations.

Based on the explanation above, extensive surgical debridement, decompression, or amputation is not typically indicated for acute thrombophlebitis since it can be managed conservatively unless complicated by deep vein involvement or severe local issues.