I've updated my Montero and my Volvo to HID's with ballasts, but they are not LED. In both vehicles I am running bluetooth connections to my iPhone. The Montero has an aftermarket headunit, but the Volvo has the factory headunit with a GROM Audio smartphone connection kit. Neither has any RF noise issues.
I can't imagine LED lights actually causing a problem, they are more efficient by far than Halogen or HID xeons, and I should think that efficiency would produce less RF noise. Did you use a specific harness adapter that plugs your new headunit into the existing wiring harness? If so, you really shouldn't be getting any noise unless you tapped into a power wire that is coming off the alternator instead off the battery (indirectly, but I think you know what I mean).