People's attitudes towards email apps

I’m wondering what people’s attitudes are to apps that require access to customers’ email accounts.

I am aware of some apps that’ll sync with your gasp online banking account! I’m extremely hesitant to even click the allow access to email button, but maybe I’m a little more paranoid than many.

What are some reactions you’ve seen, and your own reactions? What if any are some examples of successful apps that have gotten users to overcome this (other than email apps like Spark)?