Dehaze drastically swifts colors/white balance, how to prevent this?

Unfortunately, this is normal. What I do, is correct one image, where I like the color. Open it is PS as a smart object. Then I make a smart object via copy. I can then open that layer back up in ACR and use the dehaze, however I want. When done, I set that layer's blend mode to luminosity, in PS.

Here is an example. top is normal dehaze - overdone to make a point. Bottom is the dehaze image set to luminosity mode.

As its name implies, the primary purpose of Dehaze is to reverse the effects of atmospheric haze or fog. Some of the effects of haze are a reduction in general contrast, local contrast, and saturation, so the more you increase Dehaze, the more it uses an internal model of haze to amplify contrast and saturation. In most cases, a Dehaze value of 10 is a lot; above that, it becomes more of a blunt instrument. If you are pushing Dehaze to 50, then yes, you will see Dehaze try to restore the amount of contrast and saturation that it estimates would be lost when a subject is behind thick haze or fog. Which means, at 50, Dehaze will boost contrast and color saturation by a very high amount…by design.

If reversing haze is not the main thing you’re trying to do here, use other adjustments first. If, before applying Dehaze, the image is reasonably clear (in other words, if there is no original haze to remove), always start with the basic image corrections for general contrast: White point, black point, contrast, and the tone curve. Then, if the image still needs some more local contrast, then try Clarity and Texture. If all of those still don’t do the job, then at this point you could add a touch of Dehaze, but for normal images that aren’t hazy, a Dehaze value of around 10 to 15 is probably all that many normal images can stand before they start to look over-corrected for a non-hazy situation.

You can see how I think of this: Dehaze is the last resort, not the first. What should be done first are the basic tonal corrections. There are a lot of users who were impressed by how a quick hit of Dehaze can add snap to a image, so now they rush to use it first as a sort of one-click auto correction instead of doing the basic tonal adjustments. But in many cases they would preserve more image quality, and more subtle control over the correction, if they properly used all of the other basic tonal adjustments first.

Again, the only time Dehaze should be one of the first adjustments used is when the original is genuinely obscured by real-world haze or fog.

This is how Dehaze works – it will cause dramatic changes in the image.

I have only used with a couple of images ever (with a low setting), as a last resort when nothing else works.

If you want more contrast in the bird without changing the sky, try using Select subject and add some Clarity.

You can also use Select sky to edit the sky only. (or just duplicate and invert the bird mask)