Go to Settings>Notifications (on the left side, on my computer)>Mobile and turn that setting off. How it would get turned on by itself, I don’t know, but I’d start by checking that setting.
If it’s already set to off, then I don’t know.
On the upper/right you should see a small drop-down arrow. Click on it, and choose SETTINGS from the menu.
On the left, you should then see an option that says MOBILE. Click on that, and you should see an option to DE-ACTIVATE TEXT MESSAGING. (on mine, there is an option to ACTIVATE TEXT MESSAGING, which I have never done, and would never, ever want to do.)
You can get to this same setting on your phone as well. I don’t have an iPhone but on my Android I pulled up the FB app
Click the top left icon (looks like a person with three lines next to it)
Click [Name] View Your Profile
Click the thee dots that are to the right of Update Info and Activity Log
A box will pop up, click View Privacy Shortcuts
Click More Settings
Notifications
Mobile
Make sure everything says Turn On (which means it’s turned off), if anything says “Turn Off” click it.
Facebook has a weird habit of turning things on that were never turned on before. I’ve gotten email alerts I had turned off turned back on again.
Seems to me that they would realize that text alerts are never useful for almost anyone who has a smartphone and the Facebook app. Since 1G is dead, you always have data if you have texts.
(The "almost"s are for someone who uses the app only on Wi-fi and disables it on data, or even doesn’t actually have data. But surely that’s uncommon enough that they should have to opt in.)