Nothing’s happening, Dana. It’s just lawyers being lawyers, and being jerks (but I digress.) Because the decision was to place the promise in an oath rather than the California Rules of Professional Conduct, only truly egregious violations are likely to spur formal complaints and bar discipline. These would have to be based upon the ruled prohibiting dishonesty, not the words of the oath itself. For the vast majority of legal practitioners, the mandatory oath will only serve as a reminder of basic professional standards. There will be occasions, I assume, when a lawyer being disciplined for other rules violations may have repeated and gross incivility used to justify a harsher penalty.
Judges also have authority to punish incivility in court that they find injurious to the justice system, and their judgment—after all, they are judges—will generally be accepted. The First Amendment complaint really is a tell: any lawyer stooping to this is rejecting the concept of professionalism, which means that lawyers should behave in a manner that engenders the public trust. There is a lot of wiggle room in that pledge: the oath-taker doesn’t promise to be dignified and courteous, he or she only promises to “strive”–that is try—to be.
If you want see an example of a rough and tumble litigation style that I would defend as being within the bounds of acceptable civility, watch the performances of James Stewart and George C. Scott as the warring lawyers during the trial in “Anatomy of a Murder.” An example of a California lawyer charging over that line is in the entertaining series “Goliath,” where rogue attorney Billy Bob Thornton routinely uses “fuck” for effect while addressing the judge ad others.