This is "only" used for loans and renting, the German government is never going to query the score this company has assigned you. Social services are never impacted.
Equifax on the other hand claims:
> Social Services - When government agencies can't verify your information, you may have to wait longer to start receiving benefits.
I very much hate Schufa for the way they calculate your score (which until very recently was not even disclosed). But hey, at least they don't sell my income data to random private companies. In fact they do not have my income. Just credit related stuff. I demand an overview from them every 3 months that they have to physically mail to me, just to annoy them..
Equifax on the other hand claims:
> Social Services - When government agencies can't verify your information, you may have to wait longer to start receiving benefits.