Occurs in vanilla game, no custom textures. I looked for other open reports with "fence texture" or "stair texture" in them and nothing came up that resembled this. So far I haven't spotted any other objects that are affected by this.
Notice that this does not affect free-standing fenceposts, as shown in screenshot #3.
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This issue has been reported already. It has been linked to the original bugreport.
Please search before reporting any bugs, as it's likely that one exists already.
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I guess you missed the part where I said I already did. Thing is, I filtered out reports marked "resolved", since I assumed that meant it had already been fixed in an existing version, not a yet-to-be-released one. You may wish to consider adding a separate status for that. For a game this old, it's unrealistic to dig through reports for bugs that were fixed literally years ago to find one that still exists.