Giving a stranger your bank account number as well as your bank accounts routing number is perfectly fine and safe to do.
Whenever you write a check the check has your banks routing number on it as well as your checking account number.
So whenever you write a check to someone or a company you're giving out your bank account number as well as routing number.
The same when you have your paycheck deposited directly into your bank account.
Your employer has your bank account number and routing number on file and they have to so they can deposit your money into your account.
It is possible for someone to withdraw money through hacking your bank account with the bank account nunber as well as the routing number.
But it's not as simple as having your bank account number or routing number to take the money out of your account.
The average person cannot do much with just your bank account number or routing number.