99% sure the cross bar has no effect on the FM antenna in the glass and probably none for the Sirius antenna in the fin. RF will pass through most anything that will not conduct electricity, windows, fiberglass, wood (if not too thick) and composites and such. Running the invertor may have an appreciable effect on reception though, anything that can generate an electro-magnetic field when in use can create EMI in an RF system (electric motors are a common source).
Audio system amplifiers and speakers mounted too close or with cheaper leaky cases can do the same. Leaky RADAR detectors can cause EMI as well. If you've ran any additional wiring near-by that could be a source as well. Fix for that is route it to the other side of the vehicle (passenger) or avoid running wiring parallel to the antenna and it's power wires that feed the antenna box (if you can't avoid the antenna wiring run wires perpendicular to them instead of parallel and use high quality shielded wiring. Thinking of those add on LEDs that go where the third row seatbelt would be in other markets, that could be an issue but shouldn't effect things when turned off unless the feed voltage is PWM and sending enough power to allow the LEDs to generate noise even when not lit up?
A rear internal shelf, molle panel or accessory metal handles and other components would have an effect when the signal is trying to come in from the passenger window to get to the antenna. Having a dense full load out in the rear blocking a sight line from side to side would have a small effect as well and the effect would be greater the denser the loadout is or if metal is present in your gear.
I don't have a rack (external) or anything additional (internal) and have had no reception static in the 250 even with the rear heavily loaded out (although not fully blocking side to side or front to rear internal sight lines) the gear was above the rear seat back and about level with the headrests. Can't answer on Sirius as I've never and will never use it, and it's expired and staying that way.
As said it could be 1000s of things and can be hard to locate the source without specialized equipment to find what is being generated and at what frequency. All the high voltage cabling is another possible source as those have a potential of inducing current and EMI into smaller DC wiring if ran in parallel in close proximity, think adding a power management system with batteries (REDARC) this could potentially cause allot of EMI/RF interference. AC is notorious for inducing EMI into DC lines ran in parallel alongside the AC wiring as the AC wiring can generate an electromagnetic field around it, the reason most AC power cords on electronics have a ferrite core built into the supply line.
Proper and additional grounding and ferrite cores can take care of allot of it if you can find the source. If your experiencing AM/FM and Sirius interference that would be considered broad spectrum interference and in that case I'd say the interference is coming from the electrical side of things and not likely a rack or other metallic accessory around the antennas, in this case you'd have to find a spot with allot of static where say a standalone radio or different vehicle can achieve crystal clear signals and begin isolating electrical systems and components to have a fighting chance. Additional window tint can play a role too depending upon material content as some have metallic content present.