There are two main differences. Netflix is working on your behalf. Connections initiated from netflix are no different from connections initiated from your web browser or your email client. Your use of the internet, for you, is authorized. With a proxy you have no idea who is connected or what they are doing with that connection. That network activity uses you, but isn't by you, or for you.

Finally, netflix isn't likely to be hacking, spamming, or attempting to bypass bans or IP blacklists over that connection, but those are exactly the kinds of activities that shady residential proxies are used for. You basically backdoored your own computer, and now access to the internet through it will be sold to people who want to use it for something that they couldn't get away with by using a VPN or any other legitimate provider.

Depending on the sophistication of the wifi network you may be held liable and accountable for everything that takes place over your connection, including what ever nasty things the people who bought access to your proxy get up to. If the wifi system isn't set up to keep careful track of who is using it and when the liability will fall to the entity offering the wifi access, and if that connection is repeatedly used for activity in violation of the law, or the AUP of the ISP being used, that same entity will face the repercussions. Their internet connection may be temporarily suspended, and they may even be forced to stop providing wifi access to guests entirely unless they are willing/able to spend the money needed to log and monitor who is using their connection and respond to notifications of abuse over their network as well as legal requests.