Airplane mode settings not working on my iPhone

Hey there,

If you turn on Wi-Fi or Bluetooth while you're in Airplane Mode, they'll be on the next time you use Airplane Mode, unless you turn them off while in Airplane Mode , maybe that’s the reason why you still receive call and messages

for more info See ☞ Use Airplane Mode on your iPhone, iPad, iPod touch, and Apple Watch - Apple Support

Are you using wi-fi calling? Depending on how your turn on Airplane mode, and what was on the last time you did that, your connection to wi-fi remains on when you turn on Airplane mode, so iMessage will still work if wi-fi is on, and wi-fi calling as well.