Whether they can make money selling tshirts with his band's logo is as relevant to their career as musicians as is whether they can make money selling cupcakes on the side.
No, they are merchants of whatever it is they actually sell. If that's cupcakes, then it's cupcakes.
They might be merchants of whatever in order to financially support music. That's what makes them musicians, not the particular set of wares they are selling.
Nah, they're not merchants. Merchants deal in goods. Live music is a service, just like legal advice or being a security guard. Recordings of music are goods, but the music itself is not.
Whether they can make money selling tshirts with his band's logo is as relevant to their career as musicians as is whether they can make money selling cupcakes on the side.