It's unlikely that this would be a problem. Yes, coins that you send to a mixing service might end up in sketchy transactions. But they are, by definition, going through an intermediary. It's not that your coins are being sent to a drug dealer. Your coins are going to the mixing service. And then the mixing services are sending new completely transactions to that dealer.
So, it would be like the cops showing up at your door complaining that the $20 you spent at the shoe store was later used to buy drugs. I would hope that any police that were smart enough to try to trace the origin of a BTC would also understand the idea that you can't control the other transactions in a mixing service.
Now, there might be some suspicion just because you are using a mixing service. I haven't heard of any cases of this, but it wouldn't surprise me to find out that police would give a drug suspect a hard time about spending BTC through a mixer. But (at least in the US) I can't imagine this being used to harass you unless you were already under suspicion for some other reason. In part, because using a mixer isn't even that obvious: it just looks like any other BTC address. The government would have to be watching your browser or browser history to know you were visiting mixer websites.