I have already done some analysis of the bug and discovered the following:

In io_scene_x3d/export_x3d.py down by line 750, when the vertices that get duplicated are being stored in vert_tri_list, the key that is stored in vertex_hash is a tuple containing the uv coordinates of that vertex. From my observation there seems to be a risk of some of the faces that are enumerated over that contain the same edges having slightly different UV coordinates stored (which seems like it might be a float precision problem.)
The solution I am using to get around this which seems to work is to replace line 736:

mesh_faces_uv[fidx].uv[f_cnr_idx][:],

with

tuple([round(val, 7) for val in mesh_faces_uv[fidx].uv[f_cnr_idx][:]]),

Which means I'm really just rounding it down to 7 decimal points, at which point the precision error seems to go away on the meshes I have gotten the problem in.
This might not be the root cause (as it might be a bug that the UV coordinates differ) which is why I am submitting this as a bug rather than a patch.

I am also not sure if there is a reason why the UV coordinates are stored as the key instead of the vertex index (v_idx), it is possible that using that index instead of relying on the UV coordinates might be a better solution.

The workaround I described turned out to not work for cases where a split is actually intended, since any vertices that are at the same coordinates will end up being merged.
My new approach, which so far seems to work, was to still round the coordinates down to the 7th decimal but to also add the vertex id to the key when matching on uv.

So

elif is_uv:
    slot_uv = 0

    def vertex_key(fidx, f_cnr_idx):
        return (
            mesh_faces_uv[fidx].uv[f_cnr_idx][:],
        )

instead becomes

elif is_uv:
    slot_uv = 0

    def vertex_key(fidx, f_cnr_idx, v_idx):
        return (
            tuple([round(val, 7) for val in mesh_faces_uv[fidx].uv[f_cnr_idx][:]] + [v_idx]),
        )

And I then just made sure to pass in v_idx to vertex_key when looping through the faces right below in the code.

It's been a while since this was commited, anyone how can find the time to review this? Thanks

sorry to bother. Any updates on this?

any feedback would be greatly appreciated so that we can move forward with other exporter contributions for the blender community.

Sorry to bother again. Any news on this? We submitted it over a year ago.

Pushed a fix in 2.8's version of the add-on now, based on your solution. No need to use the vertex index though, keys are used in a per-vertex context already.