The only hospital in DC that has a union is Washington Hospital Center. Providence definitely does NOT have a union. But, given the poor state of their facilities, the worst pay in the district, and many, many other shortcomings, they probably deserve a union more than any other hospital.
You can't opt out of the union in a union facility. Its a condition of employment. You were just a non participating member. I was at WHC, and the union dues were negligable. $40/month or something similar. WHC used to be a great hospital from talking to people that have been there forever, but all they care about is being cheap (not frugal). 1/2 the nurses there are agency/travel--being paid $100+/hr. I'm not saying the nurses make that much, but the agency is paid that much or more and then pays the nurses.
you don't have to pay union dues, but $ still comes out of your paycheck for something else if you don't (i forget what exactly). also, WHC is NOT the only hospital in DC with a union; CNMC is unionized, too.