Although the Demon Slayer Monk's words are disrespectful and indeed deserve punishment, it's not a reason for the Six Great Sects to take action.
If they strike here, they can later justify to the court that it was an impulsive act due to anger, leaving the court no reason to retaliate.
However, if they pursue him now, it's a different story. Pursuing him would mean deliberately rebelling against the court, showing disrespect. When questioned later by the court, they would be hard-pressed to defend their actions.
Although the relationship between the court and the Six Great Sects is much like what the Demon Slayer Monk described: a mutual exploitation with neither side regarding the other as a true friend.
Such matters are understood internally, but outward appearances must not reveal this.
Otherwise, what difference would you be to the Demon Slayer Monk?
