If a runner and a fielder collide, both on the move, but neither looking at each other, what's the call? My gut feeling is that the runner is called for interference if the fielder's making a play on a batted ball, but the fielder is called for obstruction otherwise.

Is that right?

Sounds reasonable, given the limited information. Definitely, if the fielder is fielding a batted ball and collides with a runner then we have interference. In OBR there would need to be a play being made on the runner for obstruction to be called. Example, SS and R2 collide on a ball hit to 2B, who throws to 1B. Collision between SS and R2 is nothing in this case.

Oh really?

You might re-read 7.06b, They call this "Type B" obstruction. The award is is not an automatic min. of one base and is dependent on the umpires judgement.
Yes in your case if R2 makes it to third there is nothing, but it still was obstruction and a delayed dead ball.

There is limited information provided. In my judgement, there is no obstruction in the example I provided, and yes, I assumed R2 would make it to 3B while 2B man is throwing out BR.

I would think that, in the specific example that was presented after the original post, in which the ball is hit to F4, and F6 and R2 collide, there is still obstruction, with R2 protected to 3B (automatic one base beyond last base legally obtained), but that nothing would be done after the play if R2 reaches 3B safely (delayed dead ball obstruction).

R2 going on the pitch. Ball hit behind the runner to F6 playing deep. F5 breaking toward the ball, but has no chance at the play. R2 looking over his shoulder to see if the ball leaves the infield, F5 looking out toward F6.

The collide about 6 feet from third base. Runner makes it easily to third (no fielder is there), has no chance to go home because F6 fields the ball cleanly.

Under LL or OBR this sounds like obstruction, but no bases awarded.

There's enough information to judge obstruction on 99% of plays that happen as you describe.