How compatible is a double major between philosophy and one of the natural sciences?

I think that a double philosophy/science major is a terrific idea (disclosure, I did something like that myself as an undergraduate). It lets you enjoy philosophy without giving up science, keeping your options open for when you graduate. Whether or not (and how) you can do it will depend on your institution.

Entirely! Philosophical training is an excellent complement to scientific training. Indeed, I wish more scientists had received it (see this response). The sciences abound with interesting questions for the philosopher.

A philosophy/science double major can be logistically challenging because of all the lab hours required by many science programs. But if you can make it work, I highly recommend it.

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