The Thargoids are the toughest PvE opponent we have - some call them endgame content. You must know how to deal with them or you will fail.
For fighting them, I am the wrong person to ask. As for evading, there are strategies. One is to avoid the war systems of course - don't go to the kitchen if you can't stand the heat. If you get pulled, be it a hyperdiction or an interdiction, the key feature is speed. The interceptors all can go 450 m/s, except the Basilisk, who does 530. So in an ideal world, you ship should be faster than this.
The intereptors need a moment to line up their attack. This gives you crucial seconds to mount your escape. For reference, I run evac missions in a 470 479 m/s Python (it permaboosts with three pips, so I usually fly it 3-3-0) and I have yet to lose one to the murder flowers. When I get pulled, as soon as I gain control I go FA off and boost, boost, boost. Usually, after three or four boosts I am beyond 5 km. If you fail to gain distance, turn and boost past them, interceptors turn pretty slowly. Don't go in a straght line having the Thargoid right behind you, or each of their shots will hit you. Instead, try to keep them at a slight angle. If your ship is fast enough and you keep a cool head, you can evade 100% of the time.
Also, don't fly a paper plane where the Thargoids are. A good shield helps to escape, but also remember armor. For Thargoids, resistance do not matter, raw shields and armor is the key. Having good module protection in case your shields fail is also a good idea.
Really, a Thargoid-proof is not much different than a gank proof ship, and the evasion tactics are pretty much the same. Speed, decent protection and a cool head are key, and you probably need at least some engineering on your thrusters and power distributor.