A vote to strike does not mean that a strike is going to happen or that it would be soon -- if it does. The OP didn't offer too many details, but in our industry, it is just part of the process. The company and the union offer openers. The company tells the union we can't give you all that this is what we can offer. The union says "nope, not good enough," and calls for a strike vote. The union membership votes overwhelming to strike and negotiations resume -- sometimes for years. Eventually, they settle, and then a few years later, the process starts all over again.
Again, w/o knowing more details, it is hard to say. For us, our comapny could not replace us easily. It would take weeks to get people trained and certified. For my dh's work group, it was even harder.
I was also someone who never fully understood the need for unions and swore I would never join one. It didn't take long though before I fully understood the need for a union with my former employer, and I was glad to have union backing.
Again though, I think a strike vote is just part of the process. OP, the best thing you can do is stay informed. Know what the issues are and what the company is asking for and what the union is demanding. Don't fully believe everything either side has to say because the truth almost always lies somewhere in the middle.
For example, one time the company said they were not cutting pay and the union said they were. Well, who was right? Both. The company was not cutting our hourly pay rate, but they wanted to recalculate the way the hours were figured out. That resulted in us having to work more days to get in the same amount of hours. So, yes, I'd get the same amount of pay but had to work 3 extra days a month to get it which could be seen as a pay cut.
You said you would not cross a picket line. If you mean that, start saving what you can now. If it comes down to a strike, you'll be okay. If it doesn't, you'll have a nice chuck of change to splurge on something nice for yourself or to just leave in savings.