Hi Sneeringpoet,
Welcome to Apple Support Communities. We understand that you're having an issue with your iPhone changing to RTT mode. We'd like to help.
Was this the first time this issue happened? If not, does it always happen with this one other person or if it with multiple people? The reason we ask is that RTT has to be enabled on one or both of the phones for this feature to turn on. You mentioned that both devices had this feature off. Did you check out this link to confirm that all options were off: Set up and use TTY or RTT on iPhone
This feature is a carrier feature. Did you reach out to your carrier to see if they have heard any reports of this happening on other devices? This would be a good place to start.
Let us know if we can help further.
Take care!