Jdaddy, JayL and MKern, that was a poorly constructed last paragraph on my part. Wading in the redd itself can't do any good, but could do harm. In general I approach it like I said above because of that, but there is very little research on the topic. This morning I looked for the study by Bruce C. Roberts and Robert G. White "Effects of Angler Wading on Survival of Trout Eggs and Pre-emergent Fry," from 1992 but only found an abstract or brief discussion in other papers.
Historically when the fishing season lasted until Labor day and didn't resume until Spring, an often heard rationale against expanding the season was that fishing would reduce trout populations because of interference with the spawn, including egg mortality because of wading. If wading really was a significant factor, the subsequent expansion to year-round fishing should have seen a decline from this interference and egg mortality. That hasn't happened--in fact the opposite has happened, and on some of our most frequently waded streams during post-spawn/pre-hatch (i.e. Spring Creek), we have very high density. Other states have seen similar results.
Some incidental wading in redds is not likely to be signifcant to most streams, but where a redd is trampled that is likely to kill quite a few, and if that stream already has few redds, that would be a problem for that stream. I can't swear to it because I couldn't find the full article, but I think that was Brown and White's conclusion.
In PA brooks and browns eggs hatch in late Winter to Spring. If a redd is going to be waded over accidentally, this is when it is most likely to happen since people are not thinking about avoiding redds as much by this time, and the redds themselves are often not readily distinguished from the streambed like they were when they were freshly made the previous Fall. However, this may be the MOST damaging time to wade over a redd, since it is in the period just before emergence from the gravel that the young are most vulnerable to getting squashed.