Daniel, just so you know: any text message you send from your iPhone to another iPhone will, when possible, actually be routed through Appple’s servers rather than your carrier’s. Such messages will appear in blue rather than green. Unlike text messages, they are end-to-end encrypted such that Apple has no access to the contents of your messages.
As for WhatsApp, you can deny it access to your photos and it will still work. If you only want to do text messages, you can deny it access to your contacts and manually add any phone numbers you want to recieve text messages from. You won’t be able to make voice calls.