Would the president telling the military to attack “cultural sites” be a lawful order?

If POTUS or V-POTUS or any military official orders a direct attack on a cultural site whose only designation IS a cultural site that is violation of the Geneva Conventions and a war crime, thus an unlawful order. If the site has a dual purpose that is both cultural and what is considered a valid military target then no.

Context is key. If you knowingly follow an order to target and attack what you know to be a protected cultural site with zero military purpose then I would believe you would be guilty of war crimes.

Now let’s talk how low that knowledge might be expected to be knowable. Would a fire team member (E-1 to E-4) be expected to know that target X is a protected site? Doubtful. Team leader? Probably not. Squad leader? A better chance of actually knowing but again probably not fully culpable. Plt Sergeant/Plt Leader? You could begin to make an argument that they could have known. Company Commander or above? The argument becomes that they have a duty to know what are legal targets and what are not.
My opinion

Fake new from the left....

It could be a lawful order if they are used to screen, mask or house military material or conduct military operations. Here are some doctrinal references that cover valid or non-valid targeting of persons or places. I was unable to find one from the Navy- They are pretty uniform in the examples used and the scenarios they discuss.

-UNITED STATES MARINE CORPS THE BASIC SCHOOL MARINE CORPS TRAINING COMMAND CAMP BARRETT, VIRGINIA 22134-5019 LAW OF WAR/ INTRODUCTION TO RULES OF ENGAGEMENT B130936 STUDENT HANDOUT

- FIELD MANUAL *FM 27-2 NO 27-2 HEADQUARTERS DEPARTMENT OF THE ARMY WASHINGTON, DC, 23 November 1984

- LAW OF ARMED CONFLICT (LOAC) prepared by PETERSON AFB LEGAL OFFICE

- RULES OF ENGAGEMENT REFERENCE 1. CHAIRMAN OF THE JOINT CHIEFS OF STAFF INSTR. 3121.01B, STANDING RULES OF ENGAGEMENT (SROE)/STANDING RULES FOR THE USE OF FORCE (SRUF) FOR U.S. FORCES (13 June 2005). -------NOTE: This is an unclassified document describing the considerations for commanders in ROE development and is not an actual ROE. Do not post actual ROEs if you saved one from a previous deployment as they are classified documents, and should be destroyed or turned in...………..

You have to remember who we are dealing with here. These radicals would behead each and everyone of us if given the chance. They only know how to be brutal and unrelenting. Why should hamstring our military by trying to play by a different set of rules than them?

What Pres Trump does and what he says are usually different. Talk is intended for certain audiences. Actions are intended for selected physical results; also sends a message. I’m okay with not attacking holy sites or museums. Unfortunately weapons research and development may be going on at scientific sites or universities. I can see them being targets. Terrorists know our rules and exploit them by hiding military activities under schools or hospitals.

I don't think we should target cultural sites. The current Iranian government should be viewed as temporary and the cultural sites as permanent. Additionally, the Iranian cultural sites benefit people far beyond those living in Iran.

Only, he never said he would hit Iranian cultural sites.

It would depend, do they as some have said actually have military assets around those sites hoping to use them as shields. Not sure why you would hit cultural sites if they do not have a military purpose, hell go after the leadership.

IMO, yes. If one reads either the Hague Convention, which covers Cultural sites, or the Geneva Convention, one of the things that people want ignore is that to be bound by either Convention requires that the other side reciprocate in kind. In this case, this article, "Art. 11. 1. If one of the High Contracting Parties commits, in respect of any item of cultural property under special protection, a violation of the obligations under Article 9 [ Link ] , the opposing Party shall, so long as this violation persists, be released from the obligation to ensure the immunity of the property concerned. Nevertheless, whenever possible, the latter Party shall first request the cessation of such violation within a reasonable time." Have the Iranians or parties supported by the Iranians targeted other "Cultural sites"? I think we all would agree that the answer to that one is yes, even within their own country.