Neo only uses his powers against machines, shutting down the sentinels at the end of Reloaded, blowing stuff up on the way into the Machine City, and in being able to see Smith's alter-ego in the real world. None of that is incompatible with having a wireless transceiver in his brain.
The movie clearly is trying to give the impression that he is using telekinetic powers, not hacking into the robots and causing them to act as if he is using telekinetic powers.
His powers don't work on the flesh-and-blood Bane/Smith. He can't swipe the knife away from Trinity's neck at a distance. He can't easily beat Bane/Smith in a fistfight. The best he gets is to see Smith's machine form after being blinded.
All of his powers shown in the real world are against machines, never flesh-and-blood humans.
There's nothing to contradict it, either; not all the plot points have to be served up on a nice dinner plate. If it fits nicer than the matrix-within-a-matrix theories, then might as well go with that.
