Well, as stated, you need a lot of hull to fight Thargoids, especially if you're planning to try to solo one. Additoinally, at some point during the Thargie fight, you're going ot need POWERFUL normal weaponry to down it's shield in between hearts, so really if you're going thargie hunting, you are already in a pvp spec ship apart from the AX weapons.
I haven't done it yet, but I will soon, and when I do, I will use the FGS, outfitted with 3700 armor and a biweave shield that recharges in 22 secs, combined with 1 large G5 long range Plasma accelerator, 2 medium AX missiles, 2 small AX missiles, and 2 medium AX MCs. The large long range plasma accelerator combined with the armor will definitely be enough to keep a pvp fight going long enough (and painful enough for the enemy) that they will wish that he had picked an easier target, if I can't win.
If you are only taking AX weapons, you won't be able to kill the thargie, let alone a ganker.