You ever heard of Vietnam? The footprint of the chicken was used in the late '60s and early '70s to denigrate our troops. The CND adopted it in 1982.
The peace symbol has been around for a long time and is a completely inoffensive symbol these days. It means nothing more than “peace” and that is something we are all in favor of.
The "peace symbol" has been associated with British nuclear disarmament groups since 1958 and was apparently invented by a member of one of these groups.
In the 1960's the peace symbol was used by people in the US who opposed the war in Vietnam. That is not quite the same as "denigrating our troops". In any case, even at at time the peace symbol came to have the much more general meaning of favoring peace.
Apparently some people see it as being a very politically-charged symbol. I was around in the 1960s and I see it as having about as much political charge as a smiley face. That appears to be the majority opinion about it now.