I wouldn't this is why I chose a non connected financial app on my Android phone. It took me a week of try and miss to find a good one but there's no way I'm going to trust a third party with my banking info. Heck I don't even trust my bank (but admittedly I don't have a choice in the matter).
This is also why I don't seriously use Evernote. Yeah I'd love to have all my documents and bills there, but at one point you have to stop and think about the implications of a private company (in fact 2, since they're probably using AWS) knowing everything about you.