Bullshit. In California, you simply fill out a form that tells the union that you don't want any of your dues money used for political purposes. You may or may not have to do this annually, (been several years since I dealt with it) but it's the law in California and applies to state workers and their unions just like it does to "private employees" and the unions who represent them.
I represented California BU 12 several years ago, so I was pretty well trained in this at the time.
If you don't want to pay union dues...you have the option to pay "agency fees" instead. Those simply recoup the costs of bargaining on your behalf by the unions...without the pesky hassle of actual union membership. Of course, should something happen in the workplace, don't expect to be represented by the union steward or business agent...
My union requires an annual letter that must be hand delivered in the month of June, only in the month of June, or with in 30 days of being hired. New employees are not told about this and most don't even know. I was never informed of this for years.