Where there are good-quality wooden alternatives, why not have them, if you can afford them. We had a second hand plastic toy kitchen for the dses, and I have seen pictures of wooden ones, complete with lovely pans etc and drooled over them!
In reality, though, I don't think you are going to be able to keep plastic at bay throughout your dc's childhoods. I don't think you can say to everyone that they can only buy toys made of wood/natural fibres, and some would ignore you anyway.
It is also worth remembering that plastic is often lighter than wood, and so can be easier for little hands to manipulate/lift.
And if you have daughters, they are going to want dolls, and the vast majority of those are plastic - and though I have no firsthand experience, having only dses, I think you would find that most little girls want Barbie and all her stuff - and you may be able to resist to some extent (ie, not have the Barbie curtains, wallpaper, gazebo, shoes, tops, duvet cover, school bag and flask, but only have the dolls and their clothes), but you are pretty likely to end up with some.
I can think of a lot of plastic toys, too - where there aren't wooden/natural alternatives - balls, tennis racquets, bubble blowing kits, lego and duplo, model dinosaurs, fireman helmets, model kits (airfix etc), tiaras, technology toys (cd players, keyboards, anything with a computer chip) - I'm sure there is more.
Perhaps the best suggestion is to invest in attractive storeage for your dc's toys - one of those chests with wicker drawers perhaps, or a lovely wooden toy chest or a big wicker basket - so at least it can look reasonable when it is all packed away.