That means stop sincerely disclosing they are in favor of self-defense and constitutional rights

While everything you say is true, it goes even further than this.

The Menendez brother thing is in the news again, and their trial is famous for the jury being hard deadlocked. Why?

Because women unquestioningly believed their claims about being molested by their father, all the holes in that story be damned. Where the men either didn't believe it possible or found it a shaky claim, because of aforementioned holes.

And courts will go on record saying things like "we excluded any juror who didn't believe in the death penalty" or "we dressed her modestly to make her look more appealing" which is literally playing manipulation games to get verdicts without any care of evidence.