Consider a SMS firewall that:
- flattens text to ascii-256
- recompresses, noises and slightly resizes images and video
... and only then passes the message onto your real (SIM card) phone number.
This, of course, requires that you host your phone number somewhere like Twilio which has other added benefits like additional protection from SIM-jacking and being invulnerable to theft or loss of your handset, etc.
Recommended.