Public Wi-Fi at cafes, airports, and hotels carries its own risks separate from anything a proxy addresses, so it's worth being clear about what a proxy actually does in this context.
What a proxy doesn't fix
A basic proxy doesn't encrypt the connection between your device and the Wi-Fi router itself, so someone else on the same network can still potentially intercept unencrypted traffic before it even reaches your proxy — a proxy alone isn't a substitute for connection-level encryption.
Where an HTTPS proxy helps
If you're specifically using an HTTPS-capable proxy and only visiting HTTPS sites, your actual page content stays encrypted end-to-end regardless of who's on the same Wi-Fi network, which does provide real protection for that traffic specifically.
The more complete answer
For genuine protection on untrusted networks, a VPN (which encrypts everything at the device level) is generally the more appropriate tool than a proxy, which is typically scoped to a single app or protocol rather than your whole connection.