Is Chargebee safe?

No. They don't take responsbility for their mistakes and engineers are given access to your account without your explicit permission. So they aren't safe in terms of cybersecurity and privacy and they don't own up to their mistakes.

(TL;DR yes). Not sure what would be considered unsafe, but it is a very reputable brand from our experience. We've been using them for over a year and they've processed over $1M in revenue from countries across the entire globe and handle 10s of thousands of active subscriptions for us.