The truth is there's no single, simple answer.
A lot depends on amounts involved and type of affiliation, as well as jurisdictions involved (your residence/nationality and where the money comes from).
If the affiliate agreement is between you (the human) and someone else, it's usually fine up to a degree. When it stops being small enough to just be a little bit of personal side income, any financial institution may stop it and insist that you open a business account instead.
If you're running ecommerce shopping comparison websites and get commission from Amazon, Shopify, and some merchants, a few hundred to even a few thousand︀ EUR/equivalent per month is probably fine. But if it's high-risk affiliation (gambling, forex, nutra/pharma, adult),︁ questions may arise at lower amounts.