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If it's like my 93, you don't, you replace the whole thing, or at least it was like that before, maybe there are nylon inserts available now... If the washer can't just go over the threaded part of the striker you'll need to make a longitudinal cut on the nylon insert and then slide it over the pin.
The washer probably doesn't. I think mine is the same, as encho said, just cut the new one and slip it on. Maybe run a lighter over the cut part to try melting it back together?
All of the 78-96 bronco door striker bolts are designed to be able to unscrew the washer from the bolt and replace the nylon bushings. But, if its been over-tightened or has some rust this might be hard to remove. Just use some PB blaster, let it soak for a few hours. You might also need to some tools to remove the washer from the bolt, but it does come off.