Collecting in a BLM or USFS WA is generally allowed unless a Resource Management Plan for that area prohibits it. These RMPs are constantly changing so there may be disagreement in the field when you meet someone in authority. Mostly, WAs are closed that have such things as native artifacts or petroglyphs.
BLM is pretty good online at stating which WAs are expressly closed, however, they often state that a WA is closed when in fact it is open. Look at their literature for a WA in any BLM field office, it will often contradict what they say online. BLM tells people to follow the “Leave No Trace” set of principles which are actually an ethos and not a force of law, unless the RMP incorporates them as a rule of law for a WA. Again, Leave No Trace is _not_incorporated into the Wilderness Act or existing nationwide BLM policy manuals.
As you can see by this letter, BLM CA headquarters owns up to collecting and so does the USFS. I can post an image of that letter later.