There's so much wrong with that reddit post that it's hard to understand how anyone supports it. just off the top of my head without doing any sort of line by line book retorting:
1. There is no fire magic south of the wall at the time the wall was built (no targs, no dragons, no r'hllor, etc)
2. There is no fire magic anywhere, period. If we take the age of heroes at face value, the wall was built 8k years ago. This is before the Ghiscari Empire, much less Valyria. The proto-valyrians are still sheep herders at this point, if they even existed at all. There are no tamed dragons, anywhere on Earth. The ones we learn about are still living inside volcanos at this time. Even if we assume shady math due to no written record keeping and myth/lore angle, we know that the wall was built after the first men made contact with, fought, and then made peace with the Children of the Forest. So it was after the arm of Dorne was shattered which stopped the flow of the First men from Essos into Westeros. I forget what that's called, the age of legends or some shit. Anyway, at that time the children + first men encounter the others and the long night and age of heroes occurs. Then the wall is built. Then a long time after this, the Andals invade via the narrow sea, "rediscovering" westeros. It's not until after the Andal invasion that the Valyrian's discover the dragons and go from being sheep herders to magical dragon tamers and form their empire. And there is no real magic in Essos until the dragons appear, thousands of years after the Other's/long night/wall is built/etc.
3. it is mentioned that the last hero fights and wins against the others with dragonsteel, which Jon Snow interprets as Valyrian steel*. It's an additional weapon useful against them just like dragonglass (obsidian)
4. The Night's king was the 13th LC of the NW, the NW being created to guard the wall. Thus the wall existed for 12 other LCs before the Night's King.
5. The others do attack and kill wildlings all the time, they attack all men not just the NW.
6. The "hints" that the starks having blood from beyond the wall is spelled out completely with the bael the bard story from Mance, the starks aren't some other/human hybrid. They have Wildling blood in them, but since both wildlings and the rest of the "north" (including starks, excludling Manderly/white harbor) are descendants of the first men it's basically nothing.
7. The starks don't have some special affinity for "cold magic". Ned (and anyone else) can sleep in the nude in winterfell because the castle is built on a natural hot springs that pumps scorching hot water through the walls and keeps the castlevery warmeven throughout winter. That combined with the green houses is how they survive the ridiculously bad winters that exist in grrm's world and it's why winterfell is the seat of power in the north.
*yeah Valyria didn't exist at the time of the Last Hero, so it's not valyrian steel. Jon isn't exactly a student of history. unreliable narrator. Also I just think GRRM fucked this up, more than any other conspiracy theory thing. That or Valyrian's didn't invent Valyrian Steel, they are just known for it.