Movement should always be interrupted if you focus a text edit widget. It’s going to eat all the text keyboard keys until you’ve shifted focus elsewhere. That’s the behavior I would expect on any game.
As for the ‘default navigation’ rules, you can override the behavior by providing a new navigation config.
FSlateApplication::Get().SetNavigationConfig( FNavigationConfig&& Config );
Though it looks like we don’t give you the option to disable Tab for Next/Shift+Tab for Previous. Will make a note to fix that for 4.12.
To get around it now - You could pre-process the input, by registering a FSlateApplication::Get().SetInputPreProcessor(), you can use that to access any key before slate looks at it and do something else with it and prevent further handling of the key if you wish.