Calling it a "transaction" is a stretch - using that logic, Department of Commerce could ban any online download they wanted. That's clearly not a good outcome, and not an interpretation we as technologists should accept.
HN is usually in support for government interventions against big cos. We are told that the government is expressing the will of the people. Why should we encourage Apple and Google to counter the will of the people in this case?
The app stores are on your phone, the apps you should install on your property should be your decision and no government or company should have any say on this.
Its a matter of right, its a matter of freedom, and we should not just have the sad option to choose the one who we will abdicate our freedom for.
We should not fall for this false dichotomy of choice where by picking any of them, we loose our freedoms anyway, only having the freedom to choose who will pick for us.
But unfortunately the executive has been granted a lot of ambiguous and murky power under the guise of "national security" and things like that, so I wouldn't be surprised if these actions are indeed legal, but the root of the legality is something other than ITAR or OFAC.