I'm surprised Sisko had this reaction. You'd think he would have at least cooled down and reconsidered. We know from Tuvok that ritual suicide is legal and practiced on Vulcan, and from TNG that all Worf was doing was handing him the knife, which Picard was going to allow his first officer to do on board his own ship. So it must be legal to do this.
I think Sisko got a report from Odo and didn't understand what was going on, and blew his top.
Sisko's reaction is pretty true to his to character. Sisko is shown more than once to have very little patience with Klingons. Picard might have been supportive but Sisko has a different way of doing things and I can completely understand why he would be pissed with his most senior Starfleet officer killing his brother, regardless of whether it's allowed culturally or not. It's about setting a standard and expecting his officers to follow that. Personally I think Sisko was right to tell Worf to get his shit together or get the fuck off his station.
Also, killing Gowron was necessary considering he was risking the entire Alpha Quadrant to appease his ego and destroy an honorable man.