Mining claims are a federal mining claim, administered by BLM no matter if on BLM or USFS administered ground. The ban (proper term is - moratorium) on dredging in CA is a state law that is in court and awaiting action after hearings earlier this month.
Generally the USFS and BLM require following state laws and regulations in working claims, unless federal regulations are higher standards.
Some will disagree with state and federal regulations and laws concerning what you can and can't do as far as mining on a claim or prospecting open areas, but you pays your money and takes you chances.