Aside from class-specific race relations, are there any effects of class choice that will affect play later in the game?

Specifically, this question is about effects that would discourage a wannabe late-game human fighter from starting out as a human merchant.

I found it pretty easy as a merchant. The differing classes have varying effects on your racial relations, which can make can make it easier or harder. Merchants tend to have decent starting relationships while pirates are mostly hated. That affects how the natives treat you inside a system, and also how much access you have at planets.

Edit: oops - you mentioned race relations.

The other big difference I found is in the starting ship. Merchants get a fairly big (and slower) ship with a large cargo hold, while the combat-oriented classes get small ships. Not sure how you're supposed to pirate when you have no cargo room, but whatever.

That said, there's nothing preventing a Merchant from pirating, and vice verse. Relationships change based on actions so I suppose it's possible to have a universally-hated merchant and a well-liked pirate.

I believe that, as HereForTheBeer implied, there is not much late-game significance to your choice of class. The race relations will affect the entire game, but once you have money and can buy better ships and equipment, there's nothing stopping a merchant from turning into a fighter. A merchant might start with different specific skills, geared less towards fighting and more towards trading, but you can train up fighting skills as the game progresses.

(NOTE: I've only played SR1 so I'm not sure how the skills work in SR2. The rest of my answer should apply to SR2 though.)

I played a human merchant in SR2, and by the end of the game, I had all combat skills to maxium, was loaded for bear, and could free Dominator systems with just and my wingmen, so yeah, it's not so important long term.