As a retired veteran this is what I think about it.
"Should those officer in the military be disobeying the commander chiefs directives?"
Yes, as long as they are lawful orders they have too.
I think that he should be allowed to retain his Seal Trident Pin as he has earned them. These are not handed out lightly.
It seems that the push to remove his Trident Pin is based on hard feelings from the Pentagon for Trump giving Gallagher his rank back etc... I disagree with Trump in that action. He should have left it alone and went along with the military courts ruling. Reduction in Rate to E-6 and Reduction in Pay.
Yeh, but Trump didn't leave it alone, did he? Through it all, the Navy did their dead level best to cover for Gallagher. That's right. But they couldn't cover for posing with a dead adversary because, you know, there's a fucking photograph. So they had to bust him for that. And Trump makes this wahoo a hero to all the wannabee alt-right wahoos in his base.
It's something you might want to read up on just a bit before you comment-
Eddie Gallagher (Navy SEAL) - Wikipedia
en.wikipedia.org