Let's be serious here, laundering a bitcoin is as easy as trading it at an exchange for another one. Getting a wallet is as easy as generating a new one. There's no permanent record that person X had bitcoin Y, just which wallets it passed through along the way.
If your significant other works for a Three Letter Agency, then maybe it's possible they could reverse the network connection logs to the exchanges, dig through their databases and prove that you were the one who owned the coin that bought that porn. Maybe. But given how little the FBI has done with the cache of bitcash they seized, I doubt it.
So admittedly, it's not as clean as a cash business... but neither is the sex industry.