As far as I understand coins don't have a unique ID rather wallets have balances. There is not a list of serial numbers to compare against. So if you want to ensure money is not coming from a mixer you have to look at the flow graph of transactions. But this line is kind of unclear. One one extreme you could ban any wallet that has used a mixer, on the other extreme you could ban every wallet that is anywhere in the graph involved with a mixer for example someone that used a mixer sends you money for coffee, you send someone else money, and now all three of you are banned, which probably trends towards a substantial portion of the network.