I worked for a public employee union for years and I can verify that what you said was true there. Any liberal cause and they got their members out to protest.
Yes, true. SEIU is one of the biggest offenders. They get their members to do leftist protests everywhere. In the SF Bay Area, many of their members are local government employees. They also direct large amounts of union dues money towards protests. And they coordinate with other union chapters, such as AFL/CIO groups. Any complaints by workers that dues should go towards employee vs. employer disagreements only, and not to external unrelated protests, are quickly put down and the workers are targeted for reprisal by co-workers.