..the US military has very strict rules that obligate a soldier to disobey an illegal order, and there is a significant number of individuals, and their commanders, who have been prosecuted under military law for not doing so.
So you can be court-martialled for failing to obey orders, or for obeying orders.

Gee it must be great to be a grunt!

It is great indeed, Nigel!
During our basic training in the German Federal Army we were instructed that there are three kinds of orders:
1. lawful orders you must obey
2. dubious orders you must obey, but can complain afterwards
3. criminal orders you are forbidden to obey - or you are tried and sentenced.
That is very fine in theory, but difficult to decide for the poor bloody infantrist having done only eight terms at school, so all kinds were explained very thoroughly (especially 3.) and handed out in written form to think it over.
This is one of the effects of the Nuremberg Trials in our army.