The bottom line is that right now today, with no changes to anything, if you end up with coins bearing an interesting history, you take the risk of someone becoming interested in you. You cannot prevent this risk. You cannot mitigate it. If you ditch the coins, you are still part of the chain, and you may get a knock on your door from people wondering how they came to you.
You can mitigate the risk. Don't accept coins from shady people, don't use bitcoins to break the law, and keep good records of all your transactions. The latter is required for tax purposes anyway, and is greatly facilitated by bitcoin as compared to cash.
If you run a business which sells to the public, then maybe you have to deal with shady people to some extent. In that case, not using bitcoins to break the law, and keeping good records of all your transactions, becomes even more important.
On top of all that, if you do get a knock on your door, no matter how innocent you are, don't let them in if they don't have a warrant.
I must've missed the "don't accept" button in the client that rejects unknown transactions.
Oh, wait...
Also, if the matter is serious enough, they won't be asking your permission to come in, and their only knock will leave your front door on the floor of your front hallway. Please go read my first post in this thread.
We can't. But we can do what we can to protect privacy and security of the user. We can make all lists voluntary. Part of that means we have to keep pseudo-anonymity because without that anyone who doesn't like you from anywhere on the Internet could put you on a "scam" or "hack' list. Law enforcement is no better and they could target people for political reasons like with Aaron Swartz.
It turns out that privacy and security are
hard. I believe that a couple of guys are rotting in holding cells right now because they couldn't get privacy right, and they had very good reasons to try, what with every law enforcement agency in the world trying to find them and all. And unless you are collecting bitcoins to swim through like Scrooge McDuck, there will always be a link back to you.