TNG show Picard is lawful stupid so he'd obey the order, but Riker and Worf would lead the rest of the crew into a revolt and overthrow him before he could carry it out. Movie Picard wouldn't obey the order.
Sisko may or may not obey the order. Sisko was really inconsistent as the elimination of the Maquis was the notable act of lawful stupid/evil he obeyed. Again, that was really out of character given how Sisko had been portrayed for the rest of the show. If Sisko had been written consistently in regards to the Maquis he wouldn't have eliminated them.
Section 31, ofcourse, would do it. They would probably be the most successful.
The Pegasus crew from nuBSG would do it.
Colonel Quartich from Avatar would do it.
General Warfield from Starcraft would do it.
Pretty much every Federation character from the Gundam UC timeline (besides AEUG and Karaba members like Amuro and Bright) would do it, because the Federation is lawful stupid/evil. Actually, now that I think about it, pretty much every iteration of the Federation in every Gundam timeline would do it be it the 00 Federation or Gjallarhorn.
Falks from the Free Planets Alliance of LoGH would do it to try to climb up the ranks.
I will go with Romulans from Star Trek. They are already paranoid and individuals like Sela would gleefully do it.
I think the Romulans would try to capture the Jedi and experiment upon them, thinking that they could reverse engineer their Force powers through science. Once the Romluans finally realize that they can't acquire the Force through science, either one of two things will happen: either 1. they listen to the Jedi's philosophy and begin changing their ways (plausible given how some Romulan citizens listened to Spock's philosophy, and we know that not all Romulan military officers are in on the rhetoric), or 2. they will just dispose of their Jedi captives.
The Klingons would initially fight the Jedi - not because they're following orders, but because of the promise of a good fight - but would later come to view them as honorable warriors and eventually ally with them (like how in Yesterday's Enterprise, the Klingon's conflict with the Federation came to an end after witnessing the Enterprise C's valor).