My CPA has access to my Quickbooks online, DOR, and other accounts he needs in order to do our taxes. He gets copies of all of our bank statements, but there is no reason for him to have access to our bank accounts because we pay our taxes ourselves. A lot of accountants offer payroll services, so obviously they would need your business checking account info for that. I wouldn't hesitate to give my account info to him now that I know and trust him though. It's pretty easy to keep an eye on your accounts and make sure nothing weird is going on.
I think most accountants are pretty legit. They are well educated, crazy busy, and have better things to do than mess around with stealing from clients. I feel incredibly lucky to have an awesome CPA and team to help me navigate through this post-Covid tax nightmare.