As title above states, who are currently the strongest non-professional chess players? By this, I mean players who have a full-time job outside of chess. For example, I remember German GM Georg Meier mentioning in an interview in 2018 that he has a full-time job in a bank.
Up until recently, that title would have gone to Teimour Radjabov without question in my mind. Since April of 2015 until last month, he has only played 149 games. That is not many for a top-flight GM over four and a half years. That said, he just won the right to play in the Candidate's, so he may becoming more active again.
Quite a number of old GMs were musicians and engineers. GM Mark Taimanov was also famous as top concert pianist in the Soviet Union. Mikhail Botvinnik was famous for being an electrical engineer and computer scientist while also being the world champion at the same time. Dr. Ruben Fine was a Doctor of psychology. GM Helmut Pfleger of Germany is an MD.
As stated by Ian Bush, Luke McShane is considered the strongest with an outside full-time job, but I am not sure I would give him the title "of strongest non-professional GM" based solely on that as he plays a fair amount, and has played 182 games in the same time frame as I listed for Radjabov. Based on that, and the 100-point difference, I still have to go with Radjabov.
Luke McShane is one possibility. He is currently (19th Nov 2018) rated 2675, and works in the financial sector.
GM Tal Shaked is a Distinguished Engineer at Google, though he hasn't played organized chess in quite some time (but his rating puts him at #1423 in the world right now...). I was going to mention Luke McShane as well (as mentioned in another answer to this question); I'm not sure what exactly he's doing right now, his LinkedIn profile hasn't been updated since 2014.
GM Michael Adams is often listed as a top non professional GM. His current rating is 2694. I am not sure if he is officially a non professional chess player anymore, but for many years he was competing in top tournaments while being a stock trader. At one point he was even number 4 in the world and has competed in some canditates tournaments. This was often commented on in tournaments he was taking part in.
Malik Mir Sultan Khan had beaten world champion Capablanca and many other strong players. He was literally playing like a machine against Capablanca. (check out the match here). But it seems like the chess world had forgotten him forever :(
Malik Mir Sultan Khan (1905 – 25 April 1966) was the strongest chess master of his time from Asia. A servant from British India, he travelled with Colonel Nawab Sir Umar Hayat Khan (Sir Umar), his master, to Britain, where he took the chess world by storm. In an international chess career of less than five years (1929–33), he won the British Championship three times in four tries (1929, 1932, 1933), and had tournament and match results that placed him among the top ten players in the world. Sir Umar then brought him back to his homeland, where he gave up chess and returned to his humble life. David Hooper and Kenneth Whyld have called him "perhaps the greatest natural player of modern times".1 Although he was one of the world's top players in the early 1930s, FIDE, the World Chess Federation, never awarded him any title (Grandmaster or International Master).