Francis Bacon was a statesman, and Isaac Newton was a mathematician by profession.
Is it fair to say that Newton was a professional mathematician and an amateur physicist?
Amateur physicist, astronomer, author, and theologian.
and alchemist, which commanded the majority of his curiosity and written output.
... at a time when alchemy (chymistry) and science were not yet fully distinct. Also, only a tenth of his written works deal with alchemy.
Also Master of the Mint and undercover crime fighter
Not really. Academy back then was not really that diversified, and it was rare for people in the academy not to get involved in multiple philosophies.
Newton would better be qualifies as a professional academic with interests in natural philosophy and mathematics.
Newton was a paid scholar, so he was as much as possible what we would call a professionas scientist now. Francis Bacon was a heir. He did many things that could be considered full-time activities related to his social status, but they were not directly tied to his money.
If the difference between amateurs and professionals was whether they were paid or not; the article’s statements would be wholly nonsensical
What's to say the article wasn't nonsensical? It's generally a listicle of platitudes that doesn't really go deep into anything. You could summarize most of it in one sentence. Professionals look at long term consequences and constantly challenge their own biases by accepting outside commentary and criticism. That sentence encompasses most of the article. I generally expect higher quality from FS, the article on second level thinking it links to is a better example of their usual content.
The question this message answers to was about their primary income.
You are free to make your own opinion based on the facts I bring.