What kind of siding do you have? The vapor permeance of your outdoor wall assembly and the indoor conditions such as temperature and relative humidity dictate what you should do inside for vapor retardation.
The IRC has a lot of detailed information on wall assemblies, and the building science corp has the gold standard of whitepapers
here. There's also a pretty good summary article
here.
Let's assume your house has vinyl or aluminum siding over OSB or similar, with Tyvek wrapping the house. Looking at page 26 of the white paper, you can see the flow chart for zone 6. This wall assembly has greater than 1.0 perms, so following the chart you can see you class II vapor resistance. You can achieve this either by taping and finishing drywall and then applying a vapor resistant paint, or applying a smart vapor retarder to the wall studs. Kraft paper counts as this when used with fiberglass, or you can use a smart vapor retarder (SVR).
Here is an appropriate SVR that you could apply over your insulation. That is what I would do if I wanted to install plywood, because plywood will not be airtight.
As others have alluded to, there is a huge amount of misinformation on the Internet (including in this thread!), and you might not want to listen to contractors in your area either. I'd bet that very few of them have ever came back after 20 years to see if there's a moisture problem in a wall they put poly on. The building science guys do exactly that -- they build walls, they test them in a controlled environment, they make hypothesis, and they apply the scientific method to learn more about building science.