If by "text" you mean SMS messaging, then no.
That said, SMS uses mobile data. If your phone supports wifi calling, you may get wifi SMS automatically (maybe not) when you have wifi calling turned on. You would need to test that. The receiver of the SMS would still get the messages though the normal SMS system.
If by "text" you mean "instant messaging using a third-party service" which uses your internet data (wifi or mobile data), like WhatsApp and SnapChat, then yes each person needs to use the same service and the app by that service.