We know that NSAIDS can reduce protein synthesis:
http://www.kinemed.com/files/Effect_of_Ibuprofen_and.pdf

What about vitamin C and E that have some evidence that they reduce muscle damage during exercise and soreness after exercise? Turmeric can reduce muscle inflammation. Do we need the muscle inflammation for growth?

Do these types of anti-inflammatory supplemements halt protein synthesis just like NSAIDS? Or are they beneficial by improving recovery?

Do some research on high doses of fish oil and sesamin. Then you will see how too much anti-inflamation can hinder muscle growth.
This has been discusses extensively, there will be plenty to read.

The study that the NSAIDS-protein synthesis lore is based on actually only looked at ibuprofen and, here is the weird thing, the same study also found that acetaminophen, which doesn't have any anti-inflammatory effects to speak of, also seems to blunt protein synthesis after weight training. However, AFAIK, there are no studies showing the same effect from either aspirin or naproxen sodium and there are a few studies that indicate that the latter does not really interfere with post-exercise muscle metabolism much at all.

As we know from the discussions about X-factor and related supplements, getting in the way of the arachidonic acid cascade reduces inflammation and also probably reduces the hypertrophic effects from resistance exercise so fish oil and sesamin are not off the hook completely.

Thanks Benson,

Is there a consensus on how much fish oil is optimal?

Pain. 2007 Jun;129(3):279-86. Epub 2006 Dec 18. Links
Acetaminophen selectively suppresses peripheral prostaglandin E2 release and increases COX-2 gene expression in a clinical model of acute inflammation.Lee YS, Kim H, Brahim JS, Rowan J, Lee G, Dionne RA.
Pain and Neurosensory Mechanisms Branch, National Institute of Dental and Craniofacial Research, Bethesda, MD, USA.

Acetaminophen is widely used for pain management as an alternative to NSAIDs and selective COX-2 inhibitors, but its action at a molecular level is still unclear. We evaluated acetaminophen's effect on PG release and the expression patterns of genes related to PG production in a clinical model of tissue injury and acute inflammation. Subjects (119 outpatients) received either 1000 mg acetaminophen, 50 mg rofecoxib (a selective COX-2 inhibitor), 30 mg ketorolac (a dual COX-1/COX-2 inhibitor), or placebo before the surgical removal of two impacted mandibular third molars. Microdialysis was used to collect inflammatory transudate from the surgical site for measurement of PGE2 and TXB2 levels at the site of injury. Biopsies were collected to investigate the expression patterns of genes related to PG production at baseline prior to surgery and at 3 or 24 h following surgery. PGE2 release was suppressed by ketorolac, rofecoxib and acetaminophen compared to placebo at 3 h coincident with increased COX-2 gene expression in biopsies collected from the surgical site. TXB2 release was suppressed only by ketorolac. COX-2 gene expression remained elevated at 24 h with continued ketorolac and acetaminophen treatment. COX-1 gene expression was significantly down-regulated at 24 h by ketorolac, rofecoxib and acetaminophen. Acetaminophen suppression of PGE2 without inhibiting TXB2 release, when COX-2 gene expression is up-regulated, suggests that acetaminophen is a selective COX-2 inhibitor in vivo. The up-regulation of COX-2 gene and down-regulation of COX-1 gene expression suggests that acetaminophen may result in changes in COX-derived prostanoids with repeated doses.