Yes, the GPS and XM antennas are well away from each other.
No, my car came with Sirius radio so I am using the Sirius antenna instead. I just swapped the plastic connectors, pink for XM and green for Sirius.
(Unlikely Issue) Is the GPS antenna anywhere near the center of the field-of-view of the XM antenna in the direction of the sky? If so, the GPS antenna could possibly be interfering with your XM reception depending on what direction your vehicle is heading with respect to the direction to the XM/Sirius spacecraft. However, I'm guessing your OEM XM antenna is on the roof of your car, so this is unlikely. Also, these aren't exactly line-of-sight (LOS) systems...S-Band and L-Band frequencies bounce around your car, diffract, etc. quite a bit.
So, moving on to the other answer you gave....
(Likely Issues) What **EXACTLY** do you mean when you say you "swapped" the connectors? Did you have to cut or splice the actual XM antenna wire to replace the connector? Or did you use a adapter of some kind?
If you actually CUT the OEM antenna wire, you've introduced noise in the line, which will affect your XM signal strength is reduce reception. Splicing antenna or microphone wires is ALWAYS a bad idea. Too many "professional installers" (I always laugh at that term...LOL) do this all the time because they don't want to bother re-routing wires up and down car pillars, dashboards, etc. To make matters worse, a lot of these guys never took a soldering class and don't know how to properly solder (e.g., "tinning" the leads first, using the right flux/solder combo, etc.).
Moving on to even LIKELIER problems here...
The XM and Sirius broadcast frequencies are NOT exactly the same. Using an antenna from one service for the other is a BAD idea. As a reference, here are the broadcast bands used by each service:
XM: 2332.5 to 2345.0 MHz (12.5 MHz bandwidth)
Sirius: 2320.0 to 2332.5 MHz (12.5 MHz bandwidth)
...besides which, the strength of the signals from both spacecraft that reach the Earth is not the same. The two services probably expect antennas with different gains.
ALSO....is your factory antenna powered??? If so, it might be an active antenna...is it getting power since you did whatever you did to "swap" connectors? Maybe the antenna's not even being properly powered anymore.
Summary Opinion:
You've revealed that you're using a Sirius antenna with XM (really bad idea). Moreover, it sounds like you cut the antenna wire(s), which really messes with antenna signals (another bad idea). Finally, your factory antenna may be a powered, active antenna and we don't know if you cut the power connections to it (yet another bad idea, if you did that...we don't know).
So, I strongly recommend you temporarily try using a virgin, uncut, unspliced, never-modified XM (NOT Sirius) antenna mounted in a GOOD location for antennas, avoiding all the potential "gotchas" I list in my first post. Don't cut anything, don't splice anything...don't even LOOK at the antenna the wrong way. Say supportive things to it, and buy it a latte before installing it.
Let us know what happens. If it works, then you may have to go through the pain of replacing your factory antenna with a proper XM antenna and routing the wires. Or simply use/hide it in a place you like.
By the way, my buddy and I both have Audis...I had an AVIC D3 before I dumped it and I just installed an X920BT in his car. In both cases, the antennas were hidden under the top, front dashboard in a stereo speaker well (we removed the small, center front speakers in both installations. There's a metal brace under each one, which provides a suitable ground plane for the antenna. Or you could just mount it on your dash, behind the center of the windshield. These are pretty small antennas, and are pretty unobtrusive. These are the things that your typical "professional installers" don't get. Sort of like trying to mount microphones covered in sticky stuff without any air behind them...which makes the mic useless. STAY IN SCHOOL, KIDS! Learn physics! lol