I have had no issues and I have been registering on line with companies for about a dozen years now and in 'the good old days' when I was registering, very few offered a secure website (but not all required an SS# either until you approached $600).
I never have an issue giving out my banking information because that information is freely available on every check I write. The information on your check allows money to go into your account without much question. It is money being pulled out of your account that the bank has responsibility to ensure legitimacy.