Can a HOA reject a buyer, because when they previously owned in the same complex they didn't pay their dues?

I will defer to some of my other colleagues, but since no one has answered yet, I would say that the HOA could not reject you as a buyer, unless it is the HOA that owns the unit.

Very few HOAs have any right to reject the buyer of a home unless the HOA owns the property being sold. Unlike a co-op where the board does have more rights of approval, it would be quite unusual for the HOA to have a refusal right. Of course, if the old debt is still within the statute of limitation, the HOA could pursue a judgment on the old debt, and then the judgment would attach to the new home.