Yes, and...

I know everyone is having fun being outraged, but there would not be "cultural" targets on any US target list. Such sites are on a "no-strike list" and/or a "restricted target list" including all UNESCO sites and many others, incl mosques, schools, etc.

— Michael Knights (@Mikeknightsiraq) January 5, 2020

...if Donald Trump, barfly, was shouting it into the phone on "Fox&Friends," nobody would much care.

IOW:

My outrage is based on the message this sends to:

-The Iranian people
-Our allies & partners
-People (esp Americans) who don’t understand that the US military won’t target cultural sites
-People who believe the military will do whatever the president directs

— David Lapan (@DaveLapanDC) January 5, 2020

Besides, there's always plausible denial, as in:  we deny it, and claim that's plausible.

We bomb mosques, we just deny the building we bombed was a mosque. Hope this helps. pic.twitter.com/tkgLuVb9ar

— Chase (@chaseawall) January 5, 2020

And, yeah:

The fact that targeting cultural and civilian sites is impermissible is *precisely* what makes idiotic, ignorant, insane @realDonaldTrump’s statement so outrageous, and why everyone is rightfully outraged, and not having fun. https://t.co/SIfSXDGVjs

— George Conway (@gtconway3d) January 5, 2020

We keep changing what "normal" is.  But that's another problem.