PSA that EJ insightful'd this.
*shrug*
While I'm hesitant to base story conjecture on reactions to posts, I wouldn't be surprised if Hazou was slighted by it
(edit: something something, death world, something something social constructs and glue) my point was that he might be or might not be, but
Keiko was the primary target, and that Hazou and the rest of the Goketsu are hurt only by splash damage. The Clan Head is offended that his clan officiated an "untrue" marriage, and decided to write of the Goketsu clan as a whole, citing Keiko as the reason why, using her as a scapegoat reason. He held her up to all of Leaf and said "I cannot officiate any of the Goketsu, just in case they might be like
her."
Honestly, though, if the Hagoromo do have such a monopoly on religious ceremonies, their clan head just made a stupid move. He called attention to it, and let everyone know that he's willing to cut
entire clans out of a cornerstone religious/social/cultural ceremony. It won't be long before other clans wonder "am I next? Am I not strict enough for them?"
Especially if Mari begins a whisper campaign along those lines. So then the other clans will worry and fret, and if Asuma doesn't act quickly, then discord will spread in Leaf. Honestly, the Hagoromo would've been better served to hint at the possibility, and then demand appeasement in a private meeting with Hazou.
Edit: thanks for the clarification, EJ! Sorry if I came across as pedantic, petulant, or just puerile in general, I was just confused about how voting works in these situations!