Can the union spend dues money on politics that I either don care about or oppose?
Yes. In one case decided by the Supreme Court, Communications Workers v. Beck, the union was found to be spending almost 80 percent of its dues money on matters unrelated to collective bargaining, such as campaign contributions. Under the law, if workers who are not union members object to the use of their money for things that are not directly related to collective bargaining, they are entitled to a refund of the portion of their dues spent on politics and other non-bargaining activities. When non-unionized workers have attempted to get their money back, they have usually met with opposition and stonewalling from union officials.