Interesting research coming out of Uni of Cambridge. Can bitcoins be tracked? ... used to have issues with tainting the bitcoins but current technology has lead to practical ways to trace stolen bitcoins. im not sure what this means for you and me, like what happens if somehow stolen bitcoins land in my hands... but interesting nonetheless.
Video: Stolen Bitcoin Tracing - Computerphile; practical way to trace stolen bitcoins Bitcoin can be traced. It's not anonymous, everything is public.
This is not really anything new since people have been doing blockchain analysis and tracing bitcoin ever since bitcoin was used to actually trade stuff over the internet. It's hard, but with the right tools, you can definitely do it.
There is nothing you can do if "stolen" bitcoins lands in your hands, you probably won't tell and at least for now, nobody will care. It doesn't make you any less trustworthy since you're not deliberately trying to receive stolen bitcoins.