Can non-Buddhists (e.g. Christians) do Zen?
The short answer is yes.
Zen is about direct pointing at reality. It is not about subscribing to any particular belief system. For this reason, what your religious beliefs are, are not intrinsically important to it.
Many Christians and members of other faiths have practiced Zen. Some have sat with the GZG as regular members.
If you would like to read more, Wisdom Books has a section on Buddhism and Christianity which includes a number of books about Zen and Christianity.