I came across your post after a google search for "Gluten Fabry's Disease" and saw you (kinda unsurprisingly) didn't have any responses in the last several months, so I figured I'd throw in my two cents.
I have not been diagnosed with Celiac disease, but I was diagnosed with Fabry's just about 10 years ago. Fabry's is very idiosyncratic in terms of who gets which symptoms and how bad. Unlike many Fabbers I had no issues with upper GI problems but I would guess anecdotally that my neuropathic pain symptoms are worse than most (early childhood onset and requiring a high doses of drugs to keep manageable). I had had near constant lower GI problems, but those have practically been eliminated with enzyme replacement therapy (Fabrazyme).
So why am I here?
Several weeks ago I went off gluten as a shot-in-the-dark way of seeing if I could control some eczema. Well, control my eczema it didn't, but by neuropathic Fabry's pain has been cut in half! I have been in much less pain and have been much more mobile than I can recall being in years. I therefore suspect some latent gluten sensitivity impacted some of the Fabry's neuropathy, or that the Fabry's neuropathy itself is gluten sensitive.
I hope you're doing well. Good luck on your personal health journey.