They will need to follow AML/KYC compliance. What they will not need to follow is proprietary snake oil marketed under the guise of AML/KNC compliance. Take the sample link from Coinfirm I quoted above:

https://www.coinfirm.io/bitcoin/aml/17Qn3TPZJ3MrpSg6qKaxZvqFCqiB99mKKE

Coinfirm alleges that the XBT address 17Qn3TPZJ3MrpSg6qKaxZvqFCqiB99mKKE

a) "Address is close proximity to Drugs Trade"
b) "Address is connected to the Deep Web"

On the basis of these allegations they recommend "Do not transact" effectively blacklisting the XBT.

The balance on this address is 3.428912 XBT or approximately 2092.63 USD.

I will use the United States as an example  since this is one of the strictest jurisdictions when it comes to AML/KNC. First the threshold for reporting is 10,000 USD or a series of transactions totaling over 10,000 USD. I can for example cross the United Sates border carrying 2000 USD in Cash, deposit or withdraw this amount from a bank or use it to pay for goods or services with no reporting or special  AML/KNC requirements. Furthermore if it were US currency there is a very high likelihood that one or more of the bills is contaminated with drug residue making the cash in "close proximity to Drugs Trade".

The equivalent in fiat would be a company that makes detectors for drug residues in currency. They then sell their "solution" to retailers and financial institutions as a means of AMC/KNC compliance. Everyone who pays in cash is then subjected to the test and a series of questions over for example using a 20 USD bill to pay for a meal. This is of course way below any regulatory requirements, but who cares since the real market here for the detectors is small cash transactions. The company will of course protect its "intellectual property" regarding how it came to make the "close proximity to Drugs Trade" allegations. The net effect of this is a very large number of false positives with large numbers of perfectly innocent law abiding people being wrongly accused. Furthermore the accused cannot confront their accuser and the accusation could very well be completely groundless. All of this will eventually get the "solution" thrown out in court, but in the meantime the company gets to sell its snake oil compliance solution to many businesses who genuinely believe that this snake oil will help them with meeting regulatory compliance requirements.

One can of course avoid all of the above, including the multiple false accusations of perfectly innocent law abiding citizens, by making currency from a substance that does not retain drug residues when exposed to a drug.

Edit 1: We must keep in mind that the taint still applies for any amount spent from the tainted address. So my 20 USD bill example is very appropriate.

Edit 2: While the boys and girls will play with their proprietary snake oil, the men and women will focus on the real market. The perfectly innocent law abiding citizens falsely accused by the snake oil peddlers.

Edit 3: http://www.scientificamerican.com/article/cocaine-contaminates-majority-of-american-currency/