First, your not going to notice much of a difference in IQ, AF, or dynamic range. The 5D MK II does amazing for wedding photographers in low-light and large prints, and the MK III only improves on that.

With that aside, it may be more beneficial to consider the other items that will impact you as the primary user of the camera.

Build The 1D has more weather proofing and seals. While this brings more durability compared to the 5DMKIII, you won't step into the margin of difference when doing wedding photography. The 5D is weather sealed and will handle rain, snow, etc (as long as you use a weather sealed lens). Why would this difference impact you then? The weight.

Weight Unlike wildlife and sports photographers (arguably the target audience of the 1DX), you're going to be carrying this camera all day with very little tripod support. You don't have a choice to remove the battery grip. It's going to be there, 2 batteries, all the time. This is one of the biggest differences as far as user experience and I feel it's a deciding factor in favor of the 5D for weddings.

FPS You mentioned that this isn't a concern for you, but for the sake of a universal answer, there's a difference and I feel it should be mentioned. You're always going to get a better FPS with the 1D. This would be a huge deal if you were a sports photographer, but with weddings it's not going to be nearly as much of a deciding factor. The disclaimer is that a higher FPS would never hurt.

Life span You're going to get more clicks out of the 1DX, period. It's a beast. Is this a factor in your decision though? I don't think so. With both cameras, you're going to be getting a new one before you wear this one out. You're not going to be sitting on burst mode rifling out shots like it's a war zone. As a wedding photographer, you're going to be shooting so your flash can keep up. Even if you do 3 weddings a weekend, you're going to have years.

Price While you said that price isn't a factor, savings can be applied to accessories for the camera. If you have a budget for either, your best option would be buying the 5D MK III and a 7D for backup (unless you already have one). It doesn't matter which one you get, you're going to need a backup or a second camera with a different lens.

All in all, I agree with the people you've been talking to. The 1DX is a prestige thing for wedding photographers because the advantages aren't in your line of work. It'd be like me using an oversized pickup truck to commute to work. Sure, it does all the same things as an economy car and more, but I'm not using it for the extras and still paying big bucks for it.

What I would do in your situation is buy the Canon 5DMKIII, used Canon 7D, and toss in a used Canon 70-200mm f/2.8 L IS MKI that never leaves the 7D and go out to a nice dinner with the money left over.