CrossFit is not yoga. I don't think anyone would argue otherwise. You can incorporate yoga into your training, and I would definitely recommend you do so. There is a time and a place for being bendy, but this really isn't the forum for that subject matter. When it comes to lifting heavy things, or performing movements at a high intensity, this would not be the time to be hyper-mobile.
Let's look at three common movements: a handstand/handstand push up, an overhead press (strict, push press, or jerk, doesn't matter), and an American kettlebell swing. All three movements should look the same in the locked out position, except for the handstand which would be inverted like Maverick and Goose's 4g negative dive with the MiG.
Look closely at the body positioning of each of those movements. This is how they should look. What is similar about all three people? Each of them are strong and solid like a column. Phallic in nature, yes, but it shows that the finishing position is the same in all three. In each movement you see a tight midline, the rib cage stays down, and the spine stays neutral.
I've talked about this concept before in From Russian Kettlebell Swings With Love. Backbends have their place in yoga, but not under a heavy load or a repetitive high intensity movement. Save your spine by keeping your rib cage pulled down. There should be little to no hyperextension of the spine during any of these movements, or during the pull up for that matter.
Arching back during a press does not feel good. Keep doing it that way over and over again, week after week, and you're going to run into problems. If you're not able to keep your rib cage down and your spine straight during these movements then you may have some combination of chest, shoulder or scapula mobility issues. Get out that lacrosse ball and get to work. You may also be lacking in general core strength and stability, so you might need to dust off that 7 Minute Abs video while you're at it.
I'm not the first person to dissect this woman's form, but let me reiterate what others have already said. If you need to have a kip that big to perform a kipping pull up, then you're not strong enough to do a kipping pull up.
So what do you with this information? Take a video of yourself from a side view doing all four of these movements. Watch it carefully frame by frame. If you find that you've been doing these movements incorrectly, tell your ego to shut the f*ck up and go back to the basics. Decrease the weight and practice the movements slowly but correctly. You'll be better off down the road.