Unless I slow down and start flying my plane backwards. I have a lot of fun doing that. Or turning cross wind and lift the wing and watch my plane flip over. Or if I'm in a verticle climb into the wind and the plane is pushed down wind. I do let the plane have it's own way quite a bit in the wind, it's a lot of fun.
Of course you can fly backward in a strong enough wind. Nobody says the wind doesn't move the plane: the plane is carried right along with the moving mass of air. But the only wind relative to the plane is head on, just as in calm air. There is no force that can change this. The other things you mention are not caused by the wind hitting your plane. They're caused by the way you respond to the plane's motion. There is no possible way that turning crosswind and lifting the wing up will make your plane flip over. You are making it flip over by doing part of a roll. and you may be doing it unintentionally. If you are flying downwind before you turn what you're probably doing, to get a turn that looks like the turns you get in still air, is turning much more sharply: more aileron and more elevator. That's what makes you flip over. If you didn't turn more sharply, the plane's downwind motion would stretch out the turn and make it look odd,, so you "correct" for this without even thinking. That correction (or maybe the odd gust) is what flips your plane.
If you are in a full scale airplane, above the clouds so you can't see the ground, there is absolutely no way you can tell which direction a steady wind is blowing in.
Here's a nice illustration based on one that somebody used in an earlier thread. Suppose you are on the deck of an aircraft carrier, going north at 30 mph on a day when the wind is from the south at 30 mph. On the deck, you (and your model) will feel no wind at all. So you take off and fly around. Will your plane behave the way it does on a calm day at the field? Or will it "flip over" when you turn toward the east or west? It is, after all, flying in a 30 mph wind, in some sense. But, just as you can't feel that wind, neither can your plane. And if you jump off the deck into the water, you will now feel a lot of wind (until you get sucked into the props, I suppose). Does this mean your plane will now "feel the wind." Of course not.
My beginning students say all the time that the wind is doing weird things to their planes. So I have them put in some aileron trim and up elevator trim and go hands off. The plane starts turning, and doesn't stop. It doesn't turn more into or away from the wind or flip over. It just makes the turn, though not, of course, in a circle. Try it on a simulator some time: there, you can dial up a perfectly steady wind.