I imagine sharing your IBAN or local equivalent does not imply any significantly larger danger than sharing your bitcoin address, am i missing something?

The scary thing is that there are no checks on withdrawals from your account. Anyone with your account number (which is available on all checks) could in theory withdraw money from your account.

It is not as easy as it sounds. Those kind of withdraws (direct debits) needs special accounts to start with, and can be cancelled talking to the bank (during a "grace period", typically 2 weeks). The process to determine if that withdraw was legitimate is done with the money on the original account. If you have more than normal rate of "rejections", your special account will be cancelled, and could be difficult to run direct debits again...

The specifics can change from country to country, of course. I know that in the US direct debits are rare (while in Europe are quite common), so maybe the process changes.

Anyway, your bank account number is still sensitive info, as there are scams that can challenge the whole process (generating lots of direct debits, or trying to duplicate legitimate ones to go "undercover")

That would depend on the bank and country. In the UK, for example, you can set up a direct debit and withdraw funds directly, using just the bank details. But you would need to have a UK bank account to do so, and they would presumably not just allow anyone to start running direct debits.