A terrorist group that seeks to expel all non-white and non-christians from their country (such as neo-nazi groups), would be classified as what type of terrorist group?

Under the government classification for terrorism, they would be considered both;

Ethnocentric. Groups of this persuasion see race as the defining characteristic of a society, and therefore a basis of cohesion. There is usually the attitude that a particular group is superior because of their inherent racial characteristics.

and

Religious. Religiously inspired terrorism is on the rise, with a forty-three percent increase of total international terror groups espousing religious motivation between 1980 and 1995.

They could be considered a modern day hate group, based on their actions as well.