That's a nice question but I don't think we really need to be worried about it at all. As fellow members stated already I would also care less about its history. Moreover if anyhow it got transacted from the criminal history then it won't matter to me because background checks can make sure we are not the criminal! I mean there is no way we need to be that much worried. Yes, the question is entirely valid but the answer is simple and straight that its entirely based on how we have been with our transactions.
Also if its all about p2p then why not just switch to exchanges which has whole lot of mixed coins coming from all the directions.
If I purchase bitcoins via p2p, can I get some problems if the bitcoins I get were involved in some criminal activity ? If yes then how do I avoid such situation ?
Well, those bitcoins might have been transferred many many many times before they might reach you! Basically the nodes that will keep creating further will have the connection to previous transaction (input and output, multiple) giving you extra layer of security. Yup many of them will say it could be traced but not down to the seed which was involved with criminal activity, cause that’s just impossible. It’s more or less mixing the coins continuously.
If you still think you received the coins which were involved with criminal activity then just hit Chipmixer, mix your coins and you have fresh lot of coins. ChipMixer probably offers the best solution, and it's very easy to implement. But, is it possible to get even dirtier coins using ChipMixer?
I'm afraid I don't understand exactly how ChipMixer works, do all the incoming coins mix with other coins or do the coins (chips) go directly from one user to another?
May be this is also possible. Im not sure to what extent they really mix the coins and how the algorithm works but this is best practice to avoid such transactions.