If a batter hits a ball where they would otherwise safely reach first and a runner currently on a base gets tagged out due to a base running error is this considered a fielders choice?

That would depend on whether the runner that made the base running error was forced out. If there is a runner on first base and the batter hits a ground ball into left field and the runner trips and falls between first and second and the left fielder throws to second and gets the runner out, it would be considered a force out and the batter would not get credited with a hit. But if there is a runner on first base and the batter hits a ground ball into left field and the runner rounds second base too far and the left fielder throws to second and the runner is tagged out, the batter would be credited with a base hit.

Answer:

The above is incorrect. In order for the batter to receive a Fielder's Choice and not be credited with the hit, the scorer must determine that the batter would not have safely reached 1st base. In simple terms: "the fielder COULD have thrown out the batter, but CHOSE not to". In the example above, the left fielder could not have thrown out the batter at first. The batter is awarded the hit and the defense records a 7-4 put out.

A force out does not determine a Fielder's choice. If there is a runner on 2nd with 1st empty: If the batter hits a sharp ground ball to second basemen who fields the ball cleanly and attempts to throw out the runner advancing from 2nd, the batter is given the fielder's choice whether the advancing runner is safe or out at 3rd.