Final Edit: Nevermind. I’m an idiot. X-mirror was enabled in the the N Panel. Thanks to josephhansen for his quick response!
I can’t attach the file here due to being a new user, but it’s ready for upload if someone can suggest another service that’s acceptable on this forum.
All the x-axis zeroed vertices of one particular object of mine cannot be moved on the X-axis. They can only be moved on the other axes.
Modifiers have been applied. Snapping, Proportional Editing, and Shape Keys are all disabled and empty.
I believe I’ve very rarely have encountered a similar “bug” like this before a couple of times, where after working on a mesh for a while, certain vertices cannot be moved or can only be moved “out of sync” with the mouse cursor travel distance while using the Grab Tool. In this case, it’s as if the mesh still has the mirror modifier’s clipping enabled, but the modifier is applied and the modifier list is empty.
You can add the file here:
https://pasteall.org/blend/
It sounds exactly like a Mirror Modifier clipping thing to me, but that’s obviously not it. Hopefully your file will show something more 
Welcome to BA! 
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Hey. Thanks. I attempted to upload the file there in Firefox, Chrome, Microsoft Edge, but it fails to give me a link to the uploaded file. Weird.
Edit: I’m going to reset Blender to factory settings and see if it fixes it for this particular file.
Edit 2: Resetting Blender to factory settings and resaving the file, now I’ve successfully uploaded it to PasteAll. Very weird. I’ve attached it. The newly saved file seemed to have reduced in size as well, from 2.5MB to 750KB. Guess I had some extra junk in there.
https://pasteall.org/media/6/5/6544dc57bd7bec4cce07b760102d5107.blend
Got it, reproduced your problem, and found a solution:
Just turn off your X auto symmetry
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omfg…I’m so stupid! I hate that toggle sometimes…
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haha no worries happens to all of us 
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Sculpt x mirror, edit mode x mirror, global x mirror, modifier x mirror/clipping, mirrors everywhere.
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