Direct deposit is always my first choice if offered. As long as you are working with a reputable company there is no need to be so concerned. You aren't giving them any more information than you give any company when you write them a check or pay a bill via your checking account on line. When any company has a preferred payment method, those folks are usually the first to get paid, often a week or even two earlier.
Equal rights for others does not mean fewer rights for you. It's not pie.
"I prefer someone who burns the flag and then wraps themselves up in the Constitution over someone who burns the Constitution and then wraps themselves up in the flag." -Molly Ivins
Never try to teach a pig to sing. It's a waste of your time and it really annoys the pig.