Just to confirm, are you able to login on the desktop site without any issues? Can you please try deleting the app and re-installing it? Cheers.
Thanks for trying that! Do you have any other mobile devices you could try on, to see if you have the same issue there? As well, is your iPhone currently on the latest iOS update?
Same problem happened to me, I solved it.
Go to iPhone - Settings - Safari - PRIVACY&SECURITY, turn off all below 4 items including
"prevent cross-site tracking"
"block all cookies"
"fraudulent website warning"
"check for apple pay"
then reopen Safari, then you can successfully login on Shopify app on your iPhone.