However, as I read the order, it is not freezing bank accounts. It is prohibiting banks from allowing the transfer of funds to specific organizations.
It is an asset freeze (not just bank accounts) without due process.
I also find this part interesting:
"The prohibitions in subsection (a) of this section include, but are not limited to, (i) the making of any contribution or provision of funds, goods, or services by, to, or for the benefit of any person whose property and interests in property are blocked pursuant to this order, and (ii) the receipt of any contribution or provision of funds, goods, or services from any such person."
There are no words about scienter anywhere in that entire section. It therefore appears that you can be one of these "Certain Persons Who Threaten Stabilization in Iraq" just for having received a contribution of funds, even if you accept funds without knowing their source is one of these persons in section (a)(i).
It may be poor drafting, but I doubt it was accidental. By wording it without "knowingly" or "intentionally", or even "should have known", it gives "the Secretary of the Treasury, in consultation with the Secretary of State and the Secretary of Defense" complete discretion in determining who to go after.