Welcome to the community!
Since you're using an iPhone, have you verified that Send as SMS or MMS Messaging is enabled in your phone's iMessage settings? Non-iPhone devices are not able to send/receive iMessages so your device would need to send the messages as SMS and/or MMS to those devices (see here).
If that setting is enabled, have you verified that your data setting is enabled? While sending or receiving SMS does not require data to be enabled, it is required for MMS. Depending on how your settings are set, it's possible your phone is trying to send all your messages to non-iPhones as MMS. You should note that multimedia message services (MMS) are not limited to just photo or video messages. Some phones allow users to add Subject lines to their messages -- similar to the subject lines found in emails. Adding a Subject line automatically converts a SMS to MMS. Depending on the phone and its settings, a blank subject line may also still be considered a MMS. Additionally, some phones will also convert long-SMS (messages exceeding the 160 character limit) to MMS automatically.
With the exception of Wifi-calling, SMS and MMS do not get transmitted via Wifi.
If your phone isn't able to send text messages at all, you might consider verifying your phone has the proper short message service centre (SMSC) number. Fido's SMSC is +1-514-993-1123 (see here). In addition, you might also consider verifying whether your phone has the proper MMS settings. You can verify those settings here.
Hope this helps 😀