Snakes that don't have fangs have teeth may very well still bite even if they do not inject poison into you. I typically leave rat snakes and such alone as long as they are not real close to the house. For years we had a large one living in our barn so you had to be careful when you reached up on shelf, but he kept the rats down so he was welcome there.
I would kill any snake in my house or on my porches, but if I know it is not poisonous I leave them alone away from my residence.
Non- poisonous does not always mean harmless. We get some large spread Natters that are not poisonous, but will bite you nonetheless.
So far this year I have killed two copperheads and one rat snake that was right by the house. If you don’t know if it is poisonous or not I would recommend not taking a chance.
You guys must have some monster spiders to catch a snake in their web.