"...in California attorneys on either side of a case may unilaterally remove a judge if they believe the judge is prejudiced against the attorney or the defendant and that a fair and impartial trial is not possible. The disqualification is automatic and requires no showing of cause."

This cannot be allowed, otherwise it means Trump is morally and ethically right for suggesting that Judge Curiel is prejudiced against his case.

The disqualification must be done before the judge makes any rulings.

That first post is strange. A preemptory challenge (by a side in a case) of one judge under California law is available only before the judge starts ruling in the case (as the second poster notes). After that, a judge can still be disqualified for a good reason such as bias or prejudice but the reason must be shown to the satisfaction of the challenged judge or, if not, a judge from another county randomly assigned to consider the challenge. Trump's fraud case is in federal court. There is no preemptory challenge available there but there is a similar procedure for challenging a judge for such things as bias or prejudice. It is not, though, by attacking the judge in the press. Moreover, why would anyone sane actually think that a judge born in Indiana but (allegedly) "proud of his Mexican heritage" would be out to disgrace the judiciary just to "get" Trump? It actually appears to be another example of Trump's own bigotry. Either that, or Trump is just employing a tactic he learned in business: lie and stick to it.