Many shooters do something else for a living. I looked at the data about athletes participating in air rifle disciplines at ISSF World Cups in 2014 and 2015 (up to Gabala 2015, which is not included). In total 566 different athletes participated, out of which 348 indicated their professions in the athlete profiles. Out of those, 42% are students, 15% military/army and 14% athletes. All these are more or less full time sportsmen, so it means that bout 70% are full time sportsmen, and about 30% are kind of hobby shooters.
Here is a wordle of indicated professions.