If I had the day off, I would consider standing with the strikers. If I felt the company in question were being unfair, I would not use their services or product. I would not screw my current employer, co-workers, and patients by not showing up if I were scheduled that day.
Your union's job is to obtain & enforce a contract that protects your rights in exchange for your union dues. They've done their job by getting a decent contract, you do your part by paying dues. Your employer expects that by agreeing to certain concessions, they should in return have workers that show up when scheduled.
If the hospital has done their part and follows the contract and they still feel that they may have to deal with employees not showing up due to a strike, I doubt your next labor agreement will be so cushy.
