Great question — answering as the UphillTech team:
Affiliate links are not bad for SEO. Your previous site might be penalized for other things, for example spammy backlinks. There are few general things you need to consider. Use nofollow link in paid links. Google hate sponsor links because it pass pagerank, and may be your sponsor don't want to do marketing, but they want link juicy from your website. So such a links should be nofollow. With popular affliate networks like amazon and ebay, if you don't use nofollow attribute then it is fine, because Google have algorithm which detect such a thing easily like affliate anchor text (Buy from Amazon) or buy button. So such a link don't pass pagerank, and it is fine if you forgot to use nofollow...
Full answer by Goyllo: https://webmasters.stackexchange.com/a/106107 (CC BY-SA 3.0).
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