If you are against tenure, you are against the following: ... (3) due process, ...
(3) This story is in fact about due process at work. The people filing suit are against tenure and are using due process to fight it.
I really can't speak for California, but in the Northeast US ( Pensylvania and North ), Tenure == Due Process.
In my area, a new teacher ( 3years in some states, 5 in others) can be fired or "non-renewed" without a stated reason. In practice, new teachers are given good reviews mid-year and booted without comment or useful feedback. Such would-be teachers are almost unemployable after this, and the lack of feedback means that they can't work to address preceived flaws in case they do find a way to work again.
Experienced teachers can be dismissed for any legal reason. This is usually some combination of illegal activity (bank robbers can't be teachers usually), immoral behavior (porn stars are not encouraged to continue a teaching career), incompetence (yep, you can lose your job for incompetence), and insubordination (boss tells you to be on time, you aren't...). Of course, cause has to be documented. And except for the first two (illegal, immoral), a single incident is generally not sufficient grounds for action. This is good, a single parent complaint should not end a teacer's career.
The "problem" is that when ANYBODY is terminated for cause, their terminaion can be appealed in the state courts. This is not unique to teachers, but unions are in a good position financially to challenge these terminations, and so they do so nearly every time. Ex-employees of private firms generally cannot afford the legal fees to do this, and so generally don't challenge. The union provides the resources to access "due process".
The legal appeals process favors the district if the situation is well documented and if all of the rules were followed. The key to this is making sure that you have administrators with time to spend on process. A solid HR staff can help backstop this. Of course, the only thing that voters and unions agree on is that administration is a waste. And HR looks like more administration. Districts lose these cases a lot because administrators have other priorities and so don't do a great job with documentation or process.
In my current state, employees terminated for cause are not permitted to collect unemployment insurance. Private employers are more likely not to name a cause and accept the bump in their unemployment costs. This also tends to discourage lawsuits ( a bird in the hand...). School systems don't usually have this option with tenured (due process enabled) staff.
Big private companies tend to have the middle managment, HR types, and processes in place to cover themselves when they want to terminate for cause and contest unemployment. Small companies do not, but don't contest.
It's that simple.