Brand new iPhone SE is not receiving texts from anyone who doesn’t have an iPhone

The only other suggestions I have are first, go into Settings/Mobile Data/Mobile Data Options/Enable 4G (or whatever it's call in the US) and try selecting "Data Only", or if it's already selected, choose "Voice & Data", basically change them around then reboot and try and see if you get the text. If not alter back, reboot and try to get text again.

V & D allows you to get texts while you are talking, if it's not select then if you are on a call the text should arrive after the call is finished, but sometimes that can go wrong, so when you are testing make sure you are not on a call just to be on the safe side.

Another thing to try, go to Settings/Mobile Data and select "Mobile Data Network", it should look similar to below (but with your carrier settings).

Go to your carriers website and check everything is correct, you shouldn't need to do this because their carrier updates do it automatically, but again, sometimes things go wrong.

You've done all the "on device" resets, but if you have access to a computer you could try an iTunes "Restore as New", this will completely erase the old OS and data and then put a clean OS copy back on, do not restore a "BackUp" but just setup the device with your Apple ID then test again (you can always restore your backup later if required, but make sure you do not over-write it).

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

(I appreciate you have done similar but only via the device by using "Erase All Content and Settings", but that doesn't replace the OS, the iTunes method does).

If none of the above fixes, you really need to book an appointment with a Genius at your local Apple Store, because they can test for hardware issues (although I wouldn't think that is very likely because you can at least receive some texts).

Genius Bar Reservation and Apple Support Options - Apple

I really can't think of anything else to try, my guess is it's not the device but an incorrect setting, the Restore as New should sort that (a bit of a sledge Hammer to crack a nut, but may be quicker in the long run).

One last thought which I originally discounted due to the fact you can receive calls from the contact, did you "block the contact" by mistake, it shouldn't be the case but you can still check under Settings/Phone and selecting "Call Blocking & Identification".

Hope some of the above helps.

Reading through some other discussions regarding similar issue, the only user checks/attempts to get it working are what you have already done and to ensure that MMS Messaging and Send as SMS are turned on under Settings/Messages (the latter is normally for sending, but might influence incoming, who knows).

Anything else you need to discuss with your cellular provider, Text as I understand it is setup/enabled by them, so they need to check if that is still in place for your account, may be they need to send you some sort of configuration update.

Can‘t think of anything else at the moment.