The people who are "too" cautious about giving out SSN's sometime are the people who have already been victims of identity theft because they weren't cautious enough.
Employees don't have any choice about giving an SSN to an employer. We are not employees and often *do* have a choice. I use my EIN everywhere I can. Some mystery shop companies don't accept EIN's; for those I give my SSN. But I don't like it because I have no way of knowing how they are protecting it, who has access to the data, and whether the MSC is operated by honest people or not.
Even banks and our own government have data breaches; how could a mystery shop company prevent them?
I recommend using an EIN, and if your locality taxes small businesses, pay the taxes. Anyone going into business should always find out what the local laws are regarding what you plan to do and plan to comply with them. If it makes the business unprofitable -- then find a business where you can be legal *and* make money even after paying your taxes. The penalties for non-compliance once they catch you are generally a lot harsher than complying up front.
I've had a business license since 1997 when I first became self-employed doing accounting work. It costs me $50 a year (I think in one town I lived in it was $60, and I've lived near towns where the fee was $250, and another where the fee was a percentage (like one-tenth of a percent) of your gross revenues). But if you're planning to make hundreds or thousands of dollars a year in your business, it's worth it to not have to worry about someone ratting you out and being fined more than your gross income for not getting the license.
So get the EIN, get legal with your locality, and hope you make enough money to pay taxes, because the tax rate is never 100% and you get to keep the rest.
Time to build a bigger bridge.