You can strike without a union but that should be the very last resort. Long ago in the 80’s even though we had a union we went on strike several times without the unions backing. It was over a matter of ethics. The union bosses didn’t think ethics were important and wouldn’t support us, the people who paid them, despite unanimous votes to strike. The only person that broke the strike and worked was our own union delegate. We did make the management back down, I think they knew they were wrong from the start and it wasn’t about money, but it did a lot of damage to our relationship with our union, in fact many of us left to a new union after that.
Now I’m glad I’m freelance and I don’t have to put up with the petty politics of it all.