Affiliate Networks and Affiliate Programs typically do not "require" a social media following. I've never had more than a very modest use of FB and pretty much don't use the others. However, I market on FB and many of the others. The only real reason an affiliate network or a company with an affiliate program would ask about your FB page, or other social platform page, is to help them verify you are who you claim to be when applying for an account approval.
It's very rare today to find a respected network or affiliate program that doesn't require a site, a phone or Skype call, and sometimes a social page. Most always it's just for verifying you are who you claim to be. I wouldn't work with a company that just lets me sign up and start promoting without verification of me and my credentials. I do the same with vendors. I won't work with anyone without first doing my due diligence on them as well.