I know nothing about the Seer Group except that their name has been used for scams involving wire transfer of funds. I am hoping that you did not get lured into one of those.
Most legitimate mystery shopping companies REQUIRE a valid social security number to work with them and get paid. Some will allow you to add on a social security number after your first shop, some will require it somewhere before you hit $600 in fees earned. There are several reasons for requiring a valid social security number. One obviously has to do with taxes and another has to do with discouraging shoppers from signing up multiple times to attempt to beat rotation requirements for jobs. If they don't even ask for your social security number I would be very concerned.
Most legitimate mystery shopping companies ask for a date of birth to determine which shoppers meet the criteria of which clients. For example, once you hit 40 or 50 there is no reason to send you on an alcohol or tobacco compliance shop if their employees are to card anyone who "looks like they are under 35".
Education and household income have to do with shoppers who may fit the demographic profile for clients doing rent-to-own furniture or upscale automobiles.
Legitimate companies are not prying into your personal life but attempting to determine what shops may be in your area to offer you, what client profiles you fit for shops and of course routing and account numbers of your bank account are needed to pay you by direct deposit. Be aware that your routing and account numbers are on every check you write, so are obviously available out there whenever you write a check. The banks have safeguards in place to keep unauthorized deductions from your account because should that occur, the bank will need to recover the funds.