Unfortunately, there is no simple answer to this question. Because keyboard apps "see" your typing, and iOS devices can communicate over the internet, this is theoretically possible. Apple acknowledges this and the fact that it cannot possibly police third-party apps thoroughly enough to be sure it doesn't happen.
However, Apple did provide a safety mechanism, in the form of an "Allow Full Access" setting for each individual third-party keyboard you install. If you do not explicitly enable "Full Access" for a keyboard, it will be limited in certain ways to prevent malicious behavior. In particular:
- It cannot access the network.
- It cannot access the clipboard (cut/copied text).
- It cannot access the selected text.
Our goal is to provide the best possible typing experience available on your device, and nothing else. But no need to trust us -- just leave "Full Access" off if you are concerned.
For further information, please refer to Apple's documentation on the matter: