Wi-Fi owners, admins, and other prying eyes cannot read your text messages when you connect to their Wi-Fi.
If you suspect someone is seeing your texts, they use other workarounds such as spy/monitoring apps.
Most of the time (almost always, really), it is not possible to spy on someone’s text messages just by having access to the Wi-Fi connection that person used.
The exception is if you use unencrypted messaging. The thing is that nearly no one even uses such a thing these days.
The second method is if someone has installed a spyware app on your phone or device. But they can only do this if you give them physical access to your device. They won’t be able to do this just by you connecting to their Wi-Fi.
So, the original answer that someone cannot spy on your text messages through WiFi is technically accurate in nearly every imaginable scenario.
This is because text messages (SMS) are sent via your mobile cellular network that doesn’t rely on a Wi-Fi connection.
If someone wants to hack your SMS texts, they will have to rely on the vulnerability associated with the cellular network and not via Wi-Fi.
This cellular vulnerability is usually used by authorities such as the FBI. Usually, they target high-profile and most wanted individuals.
Messages you send through Wi-Fi using messengers and other chat apps won’t be readable by the Wi-Fi owner.
Most messengers and chat apps use end-to-end encryption to secure text messages.
End-to-end encryption encrypts your texts on your phone before they are sent over the internet. The texts are then decrypted on the recipient’s end.
Prying eyes won’t be able to read your texts on Wi-Fi even if they intercept them. Prying eyes on Wi-Fi can only read your messages if you use a service that doesn’t have end-to-end encryption.
The most common method someone can use to see your texts is installing a spy or monitoring app on your phone.
Usually, the person needs to have access to an unlocked phone to be able to install the app.
After everything is set, the app will forward the required information to the individual, such as texts, messages, browsing activities, and other sensitive information.
Generally, someone cannot see your text messages when you connect to their Wi-Fi. However, threat actors can use other methods that don’t rely on Wi-Fi to get your texts.