Be aware that an EIN in some areas may lead to other issues, such as business registration and licensing in your city, county or state. While in some areas this may not be an issue, we fought that battle with an EIN for a non shopping business that was run out of the home. For me, definitely I will stay with handing out my SSN. Realize that every time you write a check you are handing out your bank routing number and your account number. It is no different providing this information to a company with whom you intend to work. Unauthorized withdrawals from your account are always a bank's liability, so should not be a great source of alarm. I appreciate any company that will pay me by direct deposit.
Of course all of this is contingent upon signing with legitimate companies where you are going to their website to register and you have gotten their identification as a legitimate company from a reliable source.