If you are applying with legitimate companies, this is a secure process. It is in the companies' best interest to provide a secure process. Doing so may lessen liability. The companies want your social security number so that they can pay you and, if necessary, issue an I-9 for your income if that meets the $600 threshold. One alternative is to obtain an EIN. EIN = Employer Identification Number. Some companies accept this number instead of a social security number, and some shoppers use it for their businesses (even if they are mystery shoppers who work alone and do not have employees). Some people think that the EIN is less personal than a social security number and believe that it might be harder to hack than a social security number. You can decide what is best for you.
If you provide it on their secure website, the risk is no greater than applying for a job. In order to work or to be an independent contractor, you must provide tax information in order to legally be paid. If you are concerned about using your social security number, you can always apply for a Tax ID Number and use that instead. Do not provide your social security number in response to any emails or blind solicitations. I have been doing this for 10 years and have provided my SS # for 100+ companies, only on their websites as a part of the registration process, and I have not had any problem so far.
How safe is it to provide my SSN as part of the application process to be a shopper for a company?
The real risk is when you apply to 30, 40, 50 MSCs and they can all verify your SS number. Then you get 1 or 2 who want a faxed or email copy of your actual SS card. You get lulled into the process being secure and let your guard down and send in the non secure way. DON'T!!! If after 30 times your SS number is verified, then something is wrong with the 1 or 2 and just delete them from your list.