How do I stop my iPhone from being hacked and remotely controlled?

I’d expect this a carrier feature known as “class 0 SMS” or “flash SMS”, and your phone is likely set to receive them.

But given the photo, I can’t be certain this is flash SMS.

Rather than posting what looks like a photo of a screenshot of a photo and all this with reflections, here is how to get a screenshot on an iPhone: Take a screenshot on iPhone - Apple Support

Getting a screenshot uses the iPhone buttons, and should not dismiss the SMS message.

For the carrier setting for flash SMS, that control has been located in various places in Settings, depending on the iOS version, and on the carrier and their SIM.

Probably: Settings > Cellular or Cellular Data or Mobile Data > look for Carrier Services or SIM Applications or such > then look for a “now” or “flash” or some such other carrier-specific term, and this for whichever carrier is showing these messages. Tap that, and then look for a “Start / Stop” or ”Enable / Disable” toggle, and select Stop or Disable or whatever the carrier app calls it.

Alternatively, check with your carrier. Probably easiest to ask your carrier where they put this particular knob too, or if only they can disable this particular scourge.

Here’s the original image enlarged, cropped, and rotated, but still unfortunately about as legible as a potato.

It is not "controlling the phone".

Contact your carrier. SMS is a carrier feature. There is nothing you can do on your phone to prevent a flash sms message from being received.

The message is a scam. It is not being hacked.

FYI: The image you posted is too small to be readable.

Interesting.

I copied that image to my Desktop, then used Preview to open it and grab the text in the middle of the screen. It says

"As vezes, a maior vitória não é alcançar® o que queremos,. mas aprender • a aceitar o que a vida nos oferece com gratidão."

which, according to the macOS Translate feature, is Portuguese for

"Sometimes, the greatest victory is not to achieve® what we want, but to learn • to accept what life offers us with gratitude."

The text above that has a translation along the lines of "The Frequently Forwarded Learn more about this message Search in Internet." Then there's the title, which ends In "SMS", and the bubble graphics ... both of which suggest that this is a screen capture of a thread in the Messages application.

How is this a "hack" of any sort?

Sounds like a flash sms...

FYI: The image you posted is too small to be readable.

Not to get off-topic but with Firefox at least I find I can right-click tiny images in posts and open them to a larger size in a new tab.