Question: I have been world-building a setting where a species of advanced aliens invades Earth, only to be forced off after the humans resort to guerilla tactics. In this setting, biological life is abundant in the universe, so Earth is not unique in that regard. The aliens are advanced, but not to the point where they have outgrown the need for raw materials. In the story I have now, the reason that the aliens have not wiped out Earth yet is because using nuclear/chemical/biological weapons of mass destruction might make the earth uninhabitable for a future harvesting operation. I have not determined what resource would best fit this role. However, I have discerned that it has the following properties:

* It is inorganic
* It actually exists in real life
* It is in reasonable abundance on earth, but is rare throughout the
universe has a whole
* The material cannot be reasonably synthesized under all known laws of
physics
* It is valuable enough for an advanced civilization to fight a war
over it, but not so valuable that the civilization cannot survive without it.

Which material, if any, would best fit the above criteria?

Answer: 
The topology of this part of the universe was peculiar immediately after the big bang, and our solar system got more than its fair share of [monopoles](https://en.wikipedia.org/wiki/Magnetic_monopole).

Some of them ended up on Earth.

The aliens have magical technology that can detect them, but not manufacture them. These monopoles are extremely valuable, they can be used to manufacture several different kinds of exotic matter... and you don't even have to dig down into the core of a neutron star to get them. You just have to scrape Ohio down to the upper mantle. Or maybe northern France.

I believe that this fulfills most of your wishlist, except possibly whether they're "real". They're theoretical, we don't have any of the things yet, and are unlikely to get any soon.
A material that doesn't check most of your requirements but could still fit your use case is clean, liquid water:

Water in itself is in abundance in the universe, however not all forms of water are useful for living life.

This material can be synthesized and we can extract clean water from ice which is abundant. However, for a civilization, extracting or synthesizing water for the entire population and on such a massive scale must be incredibly expensive. We're talking about potentially terraforming entire planets for the investment to be worth it. On the other hand, finding a planet that already has large volumes of liquid water is much much more valuable and cheaper to use.

Technically your civilization cannot survive without water. However as mentioned earlier it is in abundance in the universe. What is valuable is the scale and access of liquid water that your civilization has. So a ship crashing in a planet with large ice caps may extract enough water to survive. However your civilization will need huge investments to install a settlement there.

So civilizations will go to war to create their own settlements on planets with liquid water first before getting the ones with ice caps which are more expensive to use.